diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml new file mode 100644 index 0000000..6c6bf7f --- /dev/null +++ b/.github/workflows/tests.yml @@ -0,0 +1,24 @@ +name: scientific-tests + +on: + push: + pull_request: + +jobs: + tests: + runs-on: ubuntu-latest + strategy: + matrix: + python-version: ["3.10", "3.12"] + + steps: + - uses: actions/checkout@v4 + + - uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python-version }} + + - run: python -m pip install --upgrade pip + - run: python -m pip install -r requirements.txt + - run: python scripts/run_smoke_tests.py + - run: python scripts/final_scientific_validation.py diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 index 0000000..9f5df88 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,11 @@ +# Changelog + +## 1.0.0-rc1 — 2026-08-18 + +- Added exact average-purity and residue-class ceiling implementations. +- Added the final cardinality- and residue-matched Figure 5 workflow and data. +- Replaced the old almost-prime plot with the two-panel controlled comparison. +- Added publication-level README, provenance record, citation metadata, tests, + validation, and release figure files. +- Reclassified the former “greedy” experiment as a best-of-random-candidates + exploratory calculation outside the manuscript. diff --git a/CITATION.cff b/CITATION.cff new file mode 100644 index 0000000..ddf71cd --- /dev/null +++ b/CITATION.cff @@ -0,0 +1,33 @@ +cff-version: 1.2.0 +message: "Please cite the accompanying paper and this software release." +title: "Support-size entanglement trajectories of random subset states: code and data" +version: "1.0.0-rc1" +date-released: 2026-08-18 +repository-code: "https://github.com/GoGoKo699/Subset-states" +url: "https://arxiv.org/abs/2501.06292" +license: MIT +authors: + - family-names: Lin + given-names: Ruge + affiliation: "The Hong Kong University of Science and Technology (Guangzhou)" + - family-names: Sierra + given-names: Germán + affiliation: "Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid" + - family-names: Latorre + given-names: José I. + affiliation: "Centre for Quantum Technologies, National University of Singapore" +preferred-citation: + type: article + title: "Support-size entanglement trajectories of random subset states" + year: 2026 + authors: + - family-names: Lin + given-names: Ruge + - family-names: Sierra + given-names: Germán + - family-names: Latorre + given-names: José I. + identifiers: + - type: other + value: "arXiv:2501.06292" + url: "https://arxiv.org/abs/2501.06292" diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..935b226 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2026 Ruge Lin, Germán Sierra, and José I. Latorre + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/MANIFEST_all_files.txt b/MANIFEST_all_files.txt deleted file mode 100644 index ab173cc..0000000 --- a/MANIFEST_all_files.txt +++ /dev/null @@ -1,96 +0,0 @@ -./data/peak_verification_schedule.csv -./data/table_i_peaks.csv -./.gitignore -./MANIFEST_all_files.txt -./outputs/fig1/fig1_concentration.pdf -./outputs/fig1/fig1_concentration.png -./outputs/fig1/fig1_raw.csv -./outputs/fig1/fig1_summary.csv -./outputs/fig1/fig1_zoom_raw.csv -./outputs/fig1/fig1_zoom_summary.csv -./outputs/fig2/fig2_linear_fit_summary.csv -./outputs/fig2/fig2_peak_scaling.pdf -./outputs/fig2/fig2_peak_scaling.png -./outputs/fig2/fig2_table_with_page.csv -./outputs/fig3/fig3_spectral_bulk.pdf -./outputs/fig3/fig3_spectral_bulk.png -./outputs/fig3/fig3_spectrum.csv -./outputs/fig3/fig3_spectrum_summary.csv -./outputs/fig4/fig4_approximation.pdf -./outputs/fig4/fig4_approximation.png -./outputs/fig4/fig4_summary.csv -./outputs/fig4/fig4_zoom_summary.csv -./outputs/fig5/fig5_almost_prime_unions.csv -./outputs/fig5/fig5_qft_almost_primes.pdf -./outputs/fig5/fig5_qft_almost_primes.png -./outputs/fig5/fig5_random_qft_summary.csv -./outputs/fig6/fig6_renyi.pdf -./outputs/fig6/fig6_renyi.png -./outputs/fig6/fig6_renyi_summary.csv -./outputs/fig6/fig6_renyi_zoom_summary.csv -./outputs/fig7/fig7_partition_samples.csv -./outputs/fig7/fig7_partitions.pdf -./outputs/fig7/fig7_partitions.png -./outputs/fig7/fig7_partition_summary.csv -./outputs/fig8/fig8_greedy_partitions.pdf -./outputs/fig8/fig8_greedy_partitions.png -./outputs/fig8/fig8_samples_n10.csv -./outputs/fig8/fig8_samples_n14.csv -./outputs/fig8/fig8_summary_n10.csv -./outputs/fig8/fig8_summary_n14.csv -./outputs/peak_verification/peak_verification_n10_fit.csv -./outputs/peak_verification/peak_verification_n10.pdf -./outputs/peak_verification/peak_verification_n10.png -./outputs/peak_verification/peak_verification_n10_samples.csv -./outputs/peak_verification/peak_verification_n12_fit.csv -./outputs/peak_verification/peak_verification_n12.pdf -./outputs/peak_verification/peak_verification_n12.png -./outputs/peak_verification/peak_verification_n12_samples.csv -./outputs/peak_verification/peak_verification_n14_fit.csv -./outputs/peak_verification/peak_verification_n14.pdf -./outputs/peak_verification/peak_verification_n14.png -./outputs/peak_verification/peak_verification_n14_samples.csv -./outputs/peak_verification/peak_verification_n16_fit.csv -./outputs/peak_verification/peak_verification_n16.pdf -./outputs/peak_verification/peak_verification_n16.png -./outputs/peak_verification/peak_verification_n16_samples.csv -./outputs/peak_verification/peak_verification_n18_fit.csv -./outputs/peak_verification/peak_verification_n18.pdf -./outputs/peak_verification/peak_verification_n18.png -./outputs/peak_verification/peak_verification_n18_samples.csv -./outputs/peak_verification/peak_verification_n20_fit.csv -./outputs/peak_verification/peak_verification_n20.pdf -./outputs/peak_verification/peak_verification_n20.png -./outputs/peak_verification/peak_verification_n20_samples.csv -./outputs/peak_verification/peak_verification_summary.csv -./outputs/peak_verification/peak_verification_summary.pdf -./outputs/peak_verification/peak_verification_summary.png -./README.md -./requirements.txt -./scripts/fig1_concentration.py -./scripts/fig2_peak_scaling.py -./scripts/fig3_spectral.py -./scripts/fig4_approximation.py -./scripts/fig5_qft_almost_primes.py -./scripts/fig6_renyi.py -./scripts/fig7_partitions.py -./scripts/fig8_greedy_partitions.py -./scripts/peak_scaling_verification.py -./scripts/plot_fig1_from_csv.py -./scripts/plot_fig2_from_csv.py -./scripts/plot_fig3_from_csv.py -./scripts/plot_fig4_from_csv.py -./scripts/plot_fig5_from_csv.py -./scripts/plot_fig6_from_csv.py -./scripts/plot_fig7_from_csv.py -./scripts/plot_fig8_from_csv.py -./scripts/plot_peak_verification_from_csv.py -./scripts/run_smoke_tests.py -./subset_states/core.py -./subset_states/csv_plotting.py -./subset_states/experiments.py -./subset_states/__init__.py -./subset_states/peak_fitting.py -./subset_states/plotting.py -./subset_states/tables.py -./TREE.txt diff --git a/PROVENANCE.md b/PROVENANCE.md new file mode 100644 index 0000000..72c69db --- /dev/null +++ b/PROVENANCE.md @@ -0,0 +1,100 @@ +# Numerical provenance and robustness notes + +This document records the evidence hierarchy behind the publication release. +It is intentionally more technical than the repository landing page. + +## Table I peak estimates + +`data/table_i_peaks.csv` contains the retained production estimates +$(\widehat{M}_n,\widehat{S}_n)$ for even $n=10,\ldots,30$. + +The complete intermediate global-search records for +$n=22,24,26,28,30$ were not retained. Repeating those searches with the +released dense exact-entropy implementation is computationally expensive. The +recorded point estimates are therefore preserved as historical production data, +not reconstructed raw data. + +The repository supplies `scripts/peak_scaling_verification.py`, which samples a +local window around a recorded $\widehat{M}_n$ and fits a quadratic in +$\log_2 M$. This verifies neighbourhood consistency; it is not a global +rediscovery procedure. + +## Robustness of the finite-size regressions + +Using all eleven retained rows, $n=10,\ldots,30$, + +$$ +\widehat{S}_n=0.509300\,n-0.990091, +$$ + +$$ +\log_2\widehat{M}_n=0.703541\,n-0.357734. +$$ + +Restricting the fit to the computationally accessible range +$n=10,\ldots,20$ gives + +$$ +\widehat{S}_n=0.514457\,n-1.065190, +$$ + +$$ +\log_2\widehat{M}_n=0.693450\,n-0.210116. +$$ + +The slope changes are approximately 1.01% for peak entropy and 1.43% for peak +support size. The unreconstructed larger-size rows extend the observed trend but +do not create or materially change it. Neither regression is claimed as an +asymptotic theorem. + +## Exact analytical validation + +The release exposes code for: + +- the exact fixed-cardinality ensemble-mean reduced state; +- the exact ensemble-average purity; +- the hypergeometric diagonal-entropy curve; +- the residue-class entropy ceiling + $S(A)\leq n/2-t+H_2(\mathbf{p}^{(t)})$. + +`tests/test_exact_purity_and_residue.py` and +`scripts/final_scientific_validation.py` independently check these formulas by +exhaustively enumerating all 65,535 nonempty supports at $n=4$. + +## Residue-matched reference ensembles + +For each almost-prime support $U_{N,k}$ with $k=1,2,3$, the released +Figure 5 analysis uses four nested null ensembles: + +| matched low bits $t$ | retained information | +|---:|---| +| 0 | support cardinality only | +| 1 | even/odd populations | +| 2 | populations modulo 4 | +| 3 | populations modulo 8 | + +For every $(k,t)$, 1,000 supports are independently sampled while preserving +the complete residue-count vector. The same support is evaluated in the +computational and Fourier bases, giving paired observations. Seeds are recorded +in `data/residue_matched_summary.csv`; all 12,000 paired samples are in +`data/residue_matched_samples.csv`. + +The residual deficit after matching a constraint means “not explained by the +matched information under uniform placement.” It is not claimed to be a unique +fingerprint of primality or to isolate all higher-order arithmetic correlations. + +## Figure files and generated data + +The manuscript-ready vector PDFs in `outputs/fig1/` through `outputs/fig7/` are +the files used for the final manuscript candidate. Existing historical output +CSVs in the GitHub repository may be retained when applying this release as an +overlay. Figure 5’s final raw and summary data are included directly in this +release because the constrained-null calculation is new and central to the +revised manuscript. + +## Historical best-of-random-candidates experiment + +The former “greedy” Figure 8 experiment is not part of the manuscript. It +screened independent random candidates and selected the one with the largest +mean balanced-cut entropy; it was not a greedy construction. The code is kept +under `exploratory/best_of_random_candidates/` with corrected terminology. diff --git a/README.md b/README.md index 0844865..7ec40eb 100644 --- a/README.md +++ b/README.md @@ -1,179 +1,139 @@ -# Subset-state entanglement code +# Support-size entanglement trajectories of random subset states -This repository contains the numerical code and generated data for the manuscript *Support-size entanglement trajectories of random subset states*. +Code, data, released figures, and validation for the manuscript +**“Support-size entanglement trajectories of random subset states.”** +The manuscript updates the existing preprint record [arXiv:2501.06292](https://arxiv.org/abs/2501.06292). -The code can regenerate the manuscript figures, redraw figures from existing CSV files, and perform local verification of the Table-I peak-entanglement support sizes. The full high-cost global peak search is not repeated here; instead, `scripts/peak_scaling_verification.py` verifies the tabulated peak values by sampling locally around the reported \(M_n\) values and fitting a quadratic curve in \(\log_2 M\). +Equal-positive-amplitude subset states exhibit a rise–peak–fall entanglement +trajectory as their computational-basis support grows. This repository contains +the fixed-cardinality ensemble calculations, exact-moment checks, numerical +figure scripts, and constrained reference ensembles used in the paper. -The code has two roles: +## Key results represented in this repository -1. regenerate the manuscript figures from numerical sampling; and -2. provide a transparent, local verification script for the Table-I peak values. +- Exact ensemble-mean reduced state for uniformly random supports of fixed size. +- Exact average purity across a balanced bipartition. +- Numerical rise–peak–fall trajectories and retained peak estimates through + $n=30$. +- Exact hypergeometric diagonal-entropy and residue-class entropy bounds. +- Cardinality-, parity-, mod-4-, and mod-8-matched reference ensembles for + almost-prime supports, evaluated before and after a quantum Fourier transform. -The peak values in Table I are treated as production data. The verification script samples in a window around the tabulated peak support size \(M_n\), then fits a quadratic curve in \(\log_2 M\). It is not a global rediscovery of the peaks. +The exact purity result gives the rigorous sufficient support scale -## Installation +$$ +M=2^{(2/3)n+O(1)}, +\qquad +\overline{S}_{N,M}\geq \frac{n}{2}-1-o(1). +$$ -```bash -python3 -m venv .venv -source .venv/bin/activate -python3 -m pip install -r requirements.txt -``` - -Run the smoke test: - -```bash -python3 scripts/run_smoke_tests.py -``` - -Expected output: - -```text -smoke tests passed -``` - -## Important data files - -```text -data/table_i_peaks.csv -``` - -contains the production Table-I values: - -```text -n, M_n, S_n -10, 107, 4.072 -... -30, 1836685, 14.263 -``` +## Repository map ```text -data/peak_verification_schedule.csv +subset_states/ reusable scientific routines +scripts/ figure, validation, and local-verification entry points +data/ Table I and released matched-null datasets +outputs/ manuscript-ready figures and generated outputs +tests/ lightweight and exhaustive small-system regression tests +validation/ final independent validation reports +exploratory/ historical experiments not used in the manuscript +docs/ audit and release documentation ``` -contains a modifiable schedule for the local peak checks. Edit `samples`, `points`, and `span` there, or override them from the command line. - -## Regenerate figures from computation - -Main figures: +## Quick start ```bash -python3 scripts/fig1_concentration.py -python3 scripts/fig2_peak_scaling.py -python3 scripts/fig3_spectral.py -python3 scripts/fig4_approximation.py -python3 scripts/fig5_qft_almost_primes.py +python3 -m venv .venv +source .venv/bin/activate +python3 -m pip install -r requirements.txt +python3 scripts/run_smoke_tests.py ``` -Appendix figures: +Run the independent publication validation: ```bash -python3 scripts/fig6_renyi.py -python3 scripts/fig7_partitions.py -python3 scripts/fig8_greedy_partitions.py +python3 scripts/final_scientific_validation.py ``` -The scripts write CSV data and PDF/PNG figures under `outputs/`. - -## Redraw figures from existing CSV files - -These scripts do not recompute entropy values: +Regenerate the fast deterministic figures and verify that all seven released +PDFs are present: ```bash -python3 scripts/plot_fig1_from_csv.py -python3 scripts/plot_fig2_from_csv.py -python3 scripts/plot_fig3_from_csv.py -python3 scripts/plot_fig4_from_csv.py -python3 scripts/plot_fig5_from_csv.py -python3 scripts/plot_fig6_from_csv.py -python3 scripts/plot_fig7_from_csv.py -python3 scripts/plot_fig8_from_csv.py +python3 scripts/reproduce_publication_figures.py ``` -## Figure 2 and Table-I scaling - -Figure 2 is generated directly from `data/table_i_peaks.csv`: +A reduced computational smoke run is available through: ```bash -python3 scripts/fig2_peak_scaling.py -``` - -Outputs: - -```text -outputs/fig2/fig2_peak_scaling.pdf -outputs/fig2/fig2_peak_scaling.png -outputs/fig2/fig2_table_with_page.csv -outputs/fig2/fig2_linear_fit_summary.csv +python3 scripts/reproduce_publication_figures.py --smoke ``` -The linear-fit summary contains the coefficients for \(S_n\) and \(\log_2 M_n\). - -## Local verification of Table-I peaks +The full publication computations can be launched with `--full`, but several +runs are intentionally expensive. -Use: +## Publication figures -```bash -python3 scripts/peak_scaling_verification.py --n-values 10 12 14 -``` +| Figure | Scientific content | Main script | Released output | +|---|---|---|---| +| 1 | Support-size trajectory and cut comparison | `scripts/fig1_concentration.py` | `outputs/fig1/fig1_concentration.pdf` | +| 2 | Peak entropy and support-size scaling | `scripts/fig2_peak_scaling.py` | `outputs/fig2/fig2_peak_scaling.pdf` | +| 3 | Reduced-state spectrum near the peak | `scripts/fig3_spectral.py` | `outputs/fig3/fig3_spectral_bulk.pdf` | +| 4 | Sparse and dense approximations | `scripts/fig4_approximation.py` | `outputs/fig4/fig4_approximation.pdf` | +| 5 | Cardinality and residue controls | `scripts/fig5_qft_residue_controls.py` | `outputs/fig5/fig5_qft_residue_controls.pdf` | +| 6 | Rényi trajectories | `scripts/fig6_renyi.py` | `outputs/fig6/fig6_renyi.pdf` | +| 7 | Entropy over balanced cuts | `scripts/fig7_partitions.py` | `outputs/fig7/fig7_partitions.pdf` | -This samples support sizes in a local window around the tabulated peak \(M_n\), computes the average entropy at each sampled support size, and fits a quadratic curve in \(\log_2 M\). +Figure 5 can be redrawn exactly from the released CSV files. The matched-null +raw dataset contains 12,000 paired computational/Fourier samples. -For a larger but still manageable run: - -```bash -python3 scripts/peak_scaling_verification.py --n-values 10 12 14 16 18 20 -``` +## Table I and local verification -To use one uniform setting for all selected rows: +`data/table_i_peaks.csv` stores the retained peak estimates used in the paper. +The command ```bash -python3 scripts/peak_scaling_verification.py \ - --n-values 10 12 14 16 \ - --samples 500 \ - --points 31 \ - --span 0.25 \ - --label check +python3 scripts/peak_scaling_verification.py --n-values 10 12 14 ``` -To inspect the planned workload without running it: +performs a local neighbourhood check around selected tabulated values. It is not +a reconstruction of the original global search. Full technical provenance and +the robustness comparison are documented in [PROVENANCE.md](PROVENANCE.md). -```bash -python3 scripts/peak_scaling_verification.py --all-table --dry-run -``` +## Figure 5 constrained ensembles -Outputs: +The released files are: ```text -outputs/peak_verification/peak_verification_n*_samples.csv -outputs/peak_verification/peak_verification_n*_fit.csv -outputs/peak_verification/peak_verification_n*.pdf -outputs/peak_verification/peak_verification_summary.csv -outputs/peak_verification/peak_verification_summary.pdf +data/fig5_random_qft_summary.csv +data/fig5_almost_prime_unions.csv +data/residue_matched_summary.csv +data/residue_matched_samples.csv +data/residue_entropy_bounds.csv ``` -To redraw one verification plot from CSV: +Regenerate the null samples with: ```bash -python3 scripts/plot_peak_verification_from_csv.py --n 14 +python3 scripts/run_residue_controls.py +python3 scripts/fig5_qft_residue_controls.py ``` -## Colour palette +## Reproducibility levels -The default palette is deliberately cool-toned and avoids orange/red/yellow. To modify it, edit: - -```text -subset_states/plotting.py -``` +1. **Fast:** unit tests, exact small-system checks, Figure 2, and Figure 5 redraw. +2. **Standard:** regenerate selected numerical figures with reduced or custom + workloads. +3. **Computational:** use publication defaults for the full sampling runs and + local high-dimensional peak checks. -The palette is defined in `COOL_PALETTE`. +All stochastic scripts expose seeds. The tested software environment is recorded +in `requirements-tested.txt`. -## Reproducibility notes +## Citation -- All stochastic scripts accept a `--seed` argument. -- The local peak-verification script is designed to verify the tabulated values in a neighbourhood of the known peaks, not to repeat the original high-cost global search. -- The released precomputed peak-verification outputs cover `n=10,12,14,16,18,20`. The schedule file also lists `n=22,24,26,28,30`, but those higher-dimensional checks are not precomputed in this release because the dense exact entropy calculation becomes substantially more expensive at large `n`. -- To verify the higher-`n` rows locally, use `scripts/peak_scaling_verification.py --all-table`, optionally after lowering `samples` and `points` in `data/peak_verification_schedule.csv`, or run the checks on a machine with sufficient memory and time. +Use the citation metadata in `CITATION.cff`. The preferred paper citation is the +updated arXiv record and, once available, the journal version. -### Matplotlib note +## License -The figure scripts do not import `mpl_toolkits.axes_grid1`; inset panels use `Axes.inset_axes` through `subset_states.plotting.make_inset_axis`. This avoids a common Ubuntu issue where user-site Matplotlib and system `mpl_toolkits` are mixed. For the cleanest environment, run the code inside a Python virtual environment. +The repository is released under the MIT License. See `LICENSE`. diff --git a/TREE.txt b/TREE.txt deleted file mode 100644 index c3675ef..0000000 --- a/TREE.txt +++ /dev/null @@ -1,110 +0,0 @@ -. -./data -./data/peak_verification_schedule.csv -./data/table_i_peaks.csv -./.gitignore -./MANIFEST_all_files.txt -./outputs -./outputs/fig1 -./outputs/fig1/fig1_concentration.pdf -./outputs/fig1/fig1_concentration.png -./outputs/fig1/fig1_raw.csv -./outputs/fig1/fig1_summary.csv -./outputs/fig1/fig1_zoom_raw.csv -./outputs/fig1/fig1_zoom_summary.csv -./outputs/fig2 -./outputs/fig2/fig2_linear_fit_summary.csv -./outputs/fig2/fig2_peak_scaling.pdf -./outputs/fig2/fig2_peak_scaling.png -./outputs/fig2/fig2_table_with_page.csv -./outputs/fig3 -./outputs/fig3/fig3_spectral_bulk.pdf -./outputs/fig3/fig3_spectral_bulk.png -./outputs/fig3/fig3_spectrum.csv -./outputs/fig3/fig3_spectrum_summary.csv -./outputs/fig4 -./outputs/fig4/fig4_approximation.pdf -./outputs/fig4/fig4_approximation.png -./outputs/fig4/fig4_summary.csv -./outputs/fig4/fig4_zoom_summary.csv -./outputs/fig5 -./outputs/fig5/fig5_almost_prime_unions.csv -./outputs/fig5/fig5_qft_almost_primes.pdf -./outputs/fig5/fig5_qft_almost_primes.png -./outputs/fig5/fig5_random_qft_summary.csv -./outputs/fig6 -./outputs/fig6/fig6_renyi.pdf -./outputs/fig6/fig6_renyi.png -./outputs/fig6/fig6_renyi_summary.csv -./outputs/fig6/fig6_renyi_zoom_summary.csv -./outputs/fig7 -./outputs/fig7/fig7_partition_samples.csv -./outputs/fig7/fig7_partitions.pdf -./outputs/fig7/fig7_partitions.png -./outputs/fig7/fig7_partition_summary.csv -./outputs/fig8 -./outputs/fig8/fig8_greedy_partitions.pdf -./outputs/fig8/fig8_greedy_partitions.png -./outputs/fig8/fig8_samples_n10.csv -./outputs/fig8/fig8_samples_n14.csv -./outputs/fig8/fig8_summary_n10.csv -./outputs/fig8/fig8_summary_n14.csv -./outputs/peak_verification -./outputs/peak_verification/peak_verification_n10_fit.csv -./outputs/peak_verification/peak_verification_n10.pdf -./outputs/peak_verification/peak_verification_n10.png -./outputs/peak_verification/peak_verification_n10_samples.csv -./outputs/peak_verification/peak_verification_n12_fit.csv -./outputs/peak_verification/peak_verification_n12.pdf -./outputs/peak_verification/peak_verification_n12.png -./outputs/peak_verification/peak_verification_n12_samples.csv -./outputs/peak_verification/peak_verification_n14_fit.csv -./outputs/peak_verification/peak_verification_n14.pdf -./outputs/peak_verification/peak_verification_n14.png -./outputs/peak_verification/peak_verification_n14_samples.csv -./outputs/peak_verification/peak_verification_n16_fit.csv -./outputs/peak_verification/peak_verification_n16.pdf -./outputs/peak_verification/peak_verification_n16.png -./outputs/peak_verification/peak_verification_n16_samples.csv -./outputs/peak_verification/peak_verification_n18_fit.csv -./outputs/peak_verification/peak_verification_n18.pdf -./outputs/peak_verification/peak_verification_n18.png -./outputs/peak_verification/peak_verification_n18_samples.csv -./outputs/peak_verification/peak_verification_n20_fit.csv -./outputs/peak_verification/peak_verification_n20.pdf -./outputs/peak_verification/peak_verification_n20.png -./outputs/peak_verification/peak_verification_n20_samples.csv -./outputs/peak_verification/peak_verification_summary.csv -./outputs/peak_verification/peak_verification_summary.pdf -./outputs/peak_verification/peak_verification_summary.png -./README.md -./requirements.txt -./scripts -./scripts/fig1_concentration.py -./scripts/fig2_peak_scaling.py -./scripts/fig3_spectral.py -./scripts/fig4_approximation.py -./scripts/fig5_qft_almost_primes.py -./scripts/fig6_renyi.py -./scripts/fig7_partitions.py -./scripts/fig8_greedy_partitions.py -./scripts/peak_scaling_verification.py -./scripts/plot_fig1_from_csv.py -./scripts/plot_fig2_from_csv.py -./scripts/plot_fig3_from_csv.py -./scripts/plot_fig4_from_csv.py -./scripts/plot_fig5_from_csv.py -./scripts/plot_fig6_from_csv.py -./scripts/plot_fig7_from_csv.py -./scripts/plot_fig8_from_csv.py -./scripts/plot_peak_verification_from_csv.py -./scripts/run_smoke_tests.py -./subset_states -./subset_states/core.py -./subset_states/csv_plotting.py -./subset_states/experiments.py -./subset_states/__init__.py -./subset_states/peak_fitting.py -./subset_states/plotting.py -./subset_states/tables.py -./TREE.txt diff --git a/data/README.md b/data/README.md new file mode 100644 index 0000000..26a9a9d --- /dev/null +++ b/data/README.md @@ -0,0 +1,11 @@ +# Released data + +- `table_i_peaks.csv`: retained peak estimates used in Table I and Figure 2. +- `peak_verification_schedule.csv`: default local-check workloads. +- `fig5_random_qft_summary.csv`: random-support baseline for Figure 5(a). +- `fig5_almost_prime_unions.csv`: deterministic almost-prime points. +- `residue_matched_summary.csv`: constrained-null summary statistics. +- `residue_matched_samples.csv`: all 12,000 paired constrained-null samples. +- `residue_entropy_bounds.csv`: residue populations and exact entropy ceilings. + +See `../PROVENANCE.md` for interpretation and limitations. diff --git a/data/fig5_almost_prime_unions.csv b/data/fig5_almost_prime_unions.csv new file mode 100644 index 0000000..ae32594 --- /dev/null +++ b/data/fig5_almost_prime_unions.csv @@ -0,0 +1,14 @@ +k,m,position_entropy,qft_entropy +1,1900,4.899349105104682,4.910161079890872 +2,6092,3.3840466196230876,3.4020618634009963 +3,10306,1.9895171932561069,1.9970310402329638 +4,13172,1.0749816998212463,1.076182861821274 +5,14815,0.5373701157771932,0.5377521308442479 +6,15646,0.25372718349275586,0.2545589204444965 +7,16052,0.11115455462080934,0.11116828951036509 +8,16237,0.052040736328895824,0.05202511075460042 +9,16321,0.027555868173779918,0.02755822325407225 +10,16358,0.01508334519137926,0.015081466755131525 +11,16373,0.007750414297107273,0.007750322397443896 +12,16380,0.0033374797662400688,0.0033374712643202795 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bibliography entries: none +Duplicate bibliography keys: none +Biber warnings or errors: none + +Positioning checks completed: +- Prior fixed-size random-subset moment work is cited where the exact moment section begins. +- The compressed-support result is distinguished from pseudorandomness and does not claim to rederive indistinguishability results. +- Sparse-support, constrained-ensemble, prime-state, QFT, random-matrix, Page, and Renyi references are attached to their specific scientific roles. +- No citation cluster is used to imply prior authorship of the manuscript's new exact purity or residue-ceiling results. + +STATUS: PASS diff --git a/docs/FINAL_MANUSCRIPT_REVIEW.md b/docs/FINAL_MANUSCRIPT_REVIEW.md new file mode 100644 index 0000000..777875a --- /dev/null +++ b/docs/FINAL_MANUSCRIPT_REVIEW.md @@ -0,0 +1,148 @@ +# Final target-reader and submission-level review + +**Manuscript:** *Support-size entanglement trajectories of random subset states* +**Target:** *Journal of Physics A: Mathematical and Theoretical* +**Review date:** 17 August 2026 + +## Verdict + +The manuscript is scientifically coherent, internally consistent, readable as a quantum-information paper, and ready for author-level confirmation and repository release. I found no remaining mathematical, numerical, citation, or LaTeX defect that blocks submission. + +The main result hierarchy is now clear: + +1. exact ensemble mean reduced state; +2. exact average-purity theorem; +3. rigorous near-maximal average-entanglement guarantee at support size \(2^{(2/3)n+O(1)}\); +4. finite-size rise--peak--fall von Neumann trajectory through \(n=30\); +5. sparse hypergeometric and dense separated-mode explanations; +6. cardinality- and residue-matched application to almost-prime supports. + +The paper no longer depends on the historical arithmetic framing for its identity. The almost-prime analysis functions as a controlled application of the general subset-state framework. + +## Substantive refinements made in the final pass + +### Prior-work positioning + +The exact-moment section now acknowledges recent multi-copy moment analyses of fixed-size random subset states. The manuscript states precisely that its contribution is the direct balanced-bipartition formula for the ensemble-mean reduced state and average purity, rather than implying that fixed-size subset-state moments were previously unstudied. + +The finite-size scaling section now relates the rigorous \(N^{2/3}\) support scale to known pseudorandom-subset-state regimes while explicitly distinguishing entanglement from indistinguishability. + +### Claim calibration + +The abstract now says that the estimated peak support grows exponentially while occupying a decreasing fraction of the basis **over the studied range**. It does not convert the finite-size fit into an asymptotic law. + +Single-instance results are consistently described as sampled or selected states. Figure 3 is one sampled spectrum; Figure 7 concerns two selected states. No concentration theorem is inferred from those examples. + +### Dense-side interpretation + +The dense approximation is written in the transparent form + +\[ +T_{N,M}=h_2(\lambda_{\mathrm{mf}}) + +(1-\lambda_{\mathrm{mf}}) + \left(\log_2 d-\frac{1}{2\ln2}\right), +\] + +which separates the binary mixing entropy of the coherent mode from the rescaled Page-like bulk entropy. This is algebraically identical to the previous expression. + +### Residue-matched application + +Fourier-space matched means and deficits are now explicitly defined: + +\[ +\mu_t^F(B)=\mathbb E_{A\sim\mathcal E_t(B)}S_F(A), +\qquad +\Delta_t^F(B)=\mu_t^F(B)-S_F(B). +\] + +The manuscript uses **deficit reduction** rather than causal language such as “fraction explained.” It also distinguishes two different statements: + +- the exact parity ceiling gives a guaranteed gap from the algebraic balanced maximum; +- the parity-matched null ensemble measures the residual gap from a cardinality-matched random mean. + +### Readability + +The long Section 3 heading was manually broken between “support” and “entanglement” to avoid an unattractive hyphenated section title. No substantive compression or expansion was needed elsewhere. + +## Independent scientific validation + +The final validation script exhaustively enumerated all 65,535 nonempty supports at \(n=4\). + +| Check | Maximum discrepancy or violation | +|---|---:| +| Ensemble-mean reduced matrix | \(2.07\times10^{-14}\) | +| Exact average-purity formula | \(8.88\times10^{-16}\) | +| Residue ceiling, \(t=1\) | 0 | +| Residue ceiling, \(t=2\) | 0 | +| Independent entropy implementations | \(5.55\times10^{-16}\) bits | + +The Table I regressions were reconstructed exactly: + +\[ +\widehat S_n=0.5093n-0.9900909\ldots, +\] + +\[ +\log_2\widehat M_n +=0.703540951\ldots n-0.357734368\ldots. +\] + +The Page gap and support fraction decrease monotonically across all eleven retained rows. The old and revised dense-ansatz formulas agree to \(2.66\times10^{-15}\) bits over the complete \(n=14\) support range. + +The residue-control summary reproduces the displayed residual deficits, deficit reductions, Prime-state parity ceiling, and all six finite-sample rank statements. Full numerical output is in `FINAL_SCIENTIFIC_VALIDATION.txt`. + +## Bibliography audit + +- 33 bibliography entries; +- 33 entries cited; +- no missing keys; +- no unused keys; +- no duplicate keys; +- no Biber warning or error. + +The citations are generous but role-specific. Prior work is cited for terminology, random-state benchmarks, constrained ensembles, subset-state moments, sparse supports, prime-state structure, and QFT entanglement without obscuring which propositions and theorems are new here. + +## LaTeX and PDF validation + +The clean source compiles with + +```text +pdflatex main.tex +biber main +pdflatex main.tex +pdflatex main.tex +``` + +Final status: + +- 24 A4 pages; +- approximately 5,581 body words by `texcount`; +- 189 abstract prose words, excluding its two displayed formulas; +- no unresolved citation or reference; +- no LaTeX/package warning; +- no overfull or underfull box; +- all fonts embedded; +- PDF openable and unencrypted; +- not a scanned PDF; +- all pages rendered and visually inspected; +- no clipping, overlap, black box, or broken glyph. + +## Journal fit + +The paper is best submitted as a regular **Paper** in the journal's quantum-mechanics and quantum-information section, with additional relevance to physical combinatorics, asymptotics, number theory, and random matrices. The manuscript is shorter in words than a typical long JPhysA Paper, but its 24-page review layout contains seven figures, formal results, and four proof/diagnostic appendices. Padding would reduce readability and is not recommended. + +## Author and release confirmations still required + +These are administrative or authorial decisions, not scientific defects: + +1. Confirm the author order and each current affiliation. +2. Confirm the corresponding author, current email addresses, and submission-system ORCID information. +3. Confirm the acknowledgement wording and all funder/grant identifiers. +4. Confirm the conflict-of-interest declaration. +5. Make the GitHub repository public before submission, create a release tag, and preferably archive the release with a persistent DOI. +6. Once the repository is public, change the data-availability sentence from future tense to a stable “openly available” statement and update the software citation with the release identifier. +7. Upload this manuscript as the revised version of arXiv:2501.06292 and ensure the arXiv metadata match the new title and abstract. + +## Final assessment + +After the seven confirmations above, the manuscript is suitable for submission-level packaging. No further scientific expansion is recommended before peer review. diff --git a/exploratory/best_of_random_candidates/README.md b/exploratory/best_of_random_candidates/README.md new file mode 100644 index 0000000..83837a1 --- /dev/null +++ b/exploratory/best_of_random_candidates/README.md @@ -0,0 +1,10 @@ +# Best-of-random-candidates experiment + +This historical exploratory experiment screens independently generated random +supports and retains the candidate with the largest mean entropy over balanced +cuts. It is **not** a greedy construction, is not used in the manuscript, and +should not be interpreted as an optimization algorithm. + +The original development files referred to this as a “greedy” search. They are +preserved here under an accurate name so that the historical numerical exercise +remains inspectable without being confused with the publication workflow. diff --git a/exploratory/best_of_random_candidates/best_of_random_candidates.py b/exploratory/best_of_random_candidates/best_of_random_candidates.py new file mode 100644 index 0000000..86e917a --- /dev/null +++ b/exploratory/best_of_random_candidates/best_of_random_candidates.py @@ -0,0 +1,41 @@ +#!/usr/bin/env python3 +"""Screen random supports and retain the best mean balanced-cut entropy.""" +from __future__ import annotations +import argparse +import csv +from pathlib import Path +import sys +import numpy as np +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT)) +from subset_states.core import balanced_bipartitions, entropy_from_support, random_subset, summary_stats +from subset_states.tables import PEAK_M + + +def distribution(n: int, m: int, seed: int) -> np.ndarray: + support = random_subset(n, m, np.random.default_rng(seed)) + return np.asarray([entropy_from_support(n, support, bits) for bits in balanced_bipartitions(n)], dtype=float) + + +def main() -> None: + parser = argparse.ArgumentParser() + parser.add_argument("--n", type=int, default=10) + parser.add_argument("--m", type=int, default=None) + parser.add_argument("--seed-start", type=int, default=0) + parser.add_argument("--seed-stop", type=int, default=100) + parser.add_argument("--out", type=Path, default=None) + args = parser.parse_args() + m = args.m if args.m is not None else PEAK_M[args.n] + rows = [] + for seed in range(args.seed_start, args.seed_stop): + stats = summary_stats(distribution(args.n, m, seed)) + rows.append({"seed": seed, "n": args.n, "M": m, "partition_count": stats.count, "mean": stats.mean, "std": stats.std, "minimum": stats.minimum, "maximum": stats.maximum}) + best = max(rows, key=lambda row: row["mean"]) + print(f"best seed in [{args.seed_start}, {args.seed_stop}): {best['seed']}, mean={best['mean']:.8f}") + out = args.out or Path(f"best_of_random_candidates_n{args.n}_{args.seed_start}_{args.seed_stop}.csv") + with out.open("w", newline="") as handle: + writer = csv.DictWriter(handle, fieldnames=rows[0].keys()) + writer.writeheader(); writer.writerows(rows) + +if __name__ == "__main__": + main() diff --git a/outputs/README.md b/outputs/README.md new file mode 100644 index 0000000..095ea57 --- /dev/null +++ b/outputs/README.md @@ -0,0 +1,5 @@ +# Released outputs + +The subdirectories `fig1` through `fig7` contain the manuscript-ready vector PDF +and a PNG preview for each final figure. Scripts write regenerated outputs to the +same locations unless an alternative `--outdir` is supplied. diff --git a/outputs/fig1/fig1_concentration.pdf b/outputs/fig1/fig1_concentration.pdf index 7d8467d..213d889 100644 Binary files a/outputs/fig1/fig1_concentration.pdf and b/outputs/fig1/fig1_concentration.pdf differ diff --git a/outputs/fig1/fig1_concentration.png b/outputs/fig1/fig1_concentration.png index 6c7c23b..316ec4f 100644 Binary files a/outputs/fig1/fig1_concentration.png and b/outputs/fig1/fig1_concentration.png differ diff --git a/outputs/fig2/fig2_linear_fit_summary.csv b/outputs/fig2/fig2_linear_fit_summary.csv index 24df6d6..1f62f6a 100644 --- a/outputs/fig2/fig2_linear_fit_summary.csv +++ b/outputs/fig2/fig2_linear_fit_summary.csv @@ -1,3 +1,3 @@ quantity,slope,intercept,r_value,r_squared,p_value,slope_stderr,intercept_stderr,residual_std -log2_M_n,0.7035409513877945,-0.35773436814817394,0.9999682030282631,0.9999364070675735,3.3738880705204426e-20,0.0018701927211902418,0.039229493475354774,0.03922949347534925 -S_n,0.5093,-0.9900909090909096,0.9999853972029535,0.9999707946191487,1.0171093829010784e-21,0.0009174664680158111,0.019244938991088,0.01924493899100974 +log2_M_n,0.7035409513877945,-0.35773436814817394,0.9999682030282631,0.9999364070675735,3.3738880705204426e-20,0.0018701927211902415,0.039229493475354774,0.03922949347534941 +S_n,0.5093000000000001,-0.9900909090909114,0.9999853972029539,0.9999707946191494,1.0171093827966843e-21,0.0009174664680053479,0.019244938990868522,0.01924493899100971 diff --git a/outputs/fig2/fig2_peak_scaling.pdf b/outputs/fig2/fig2_peak_scaling.pdf index 5812efd..614cfe3 100644 Binary files a/outputs/fig2/fig2_peak_scaling.pdf and b/outputs/fig2/fig2_peak_scaling.pdf differ diff --git a/outputs/fig2/fig2_peak_scaling.png b/outputs/fig2/fig2_peak_scaling.png index 8e23988..067c879 100644 Binary files a/outputs/fig2/fig2_peak_scaling.png and b/outputs/fig2/fig2_peak_scaling.png differ diff --git a/outputs/fig2/fig2_table_with_page.csv b/outputs/fig2/fig2_table_with_page.csv index 48e9c67..db464ca 100644 --- a/outputs/fig2/fig2_table_with_page.csv +++ b/outputs/fig2/fig2_table_with_page.csv @@ -1,5 +1,5 @@ n,M_n,log2_M_n,S_n,Page_exact_bits,Page_minus_S_n -10,107,6.7414669864011465,4.072,4.279474201201169,0.207474201201169 +10,107,6.741466986401147,4.072,4.279474201201169,0.207474201201169 12,276,8.108524456778168,5.108,5.2788579336132955,0.17085793361329582 14,716,9.483815777264256,6.143,6.278703844547921,0.13570384454792084 16,1873,10.871135184243045,7.176,7.278665320895993,0.10266532089599245 diff --git a/outputs/fig3/fig3_spectral_bulk.pdf b/outputs/fig3/fig3_spectral_bulk.pdf index 9b90283..60ea87d 100644 Binary files a/outputs/fig3/fig3_spectral_bulk.pdf and b/outputs/fig3/fig3_spectral_bulk.pdf differ diff --git a/outputs/fig3/fig3_spectral_bulk.png b/outputs/fig3/fig3_spectral_bulk.png index 4727910..6958cd6 100644 Binary files a/outputs/fig3/fig3_spectral_bulk.png and b/outputs/fig3/fig3_spectral_bulk.png differ diff --git a/outputs/fig4/fig4_approximation.pdf b/outputs/fig4/fig4_approximation.pdf index fab6ef7..0539f27 100644 Binary files a/outputs/fig4/fig4_approximation.pdf and b/outputs/fig4/fig4_approximation.pdf differ diff --git a/outputs/fig4/fig4_approximation.png b/outputs/fig4/fig4_approximation.png index 02a27ab..c6d6625 100644 Binary files a/outputs/fig4/fig4_approximation.png and b/outputs/fig4/fig4_approximation.png differ diff --git a/outputs/fig5/fig5_qft_almost_primes.pdf b/outputs/fig5/fig5_qft_almost_primes.pdf deleted file mode 100644 index df5a60c..0000000 Binary files a/outputs/fig5/fig5_qft_almost_primes.pdf and /dev/null differ diff --git a/outputs/fig5/fig5_qft_almost_primes.png b/outputs/fig5/fig5_qft_almost_primes.png deleted file mode 100644 index 9c1c62e..0000000 Binary files a/outputs/fig5/fig5_qft_almost_primes.png and /dev/null differ diff --git a/outputs/fig5/fig5_qft_residue_controls.pdf b/outputs/fig5/fig5_qft_residue_controls.pdf new file mode 100644 index 0000000..619b091 Binary files /dev/null and b/outputs/fig5/fig5_qft_residue_controls.pdf differ diff --git a/outputs/fig5/fig5_qft_residue_controls.png b/outputs/fig5/fig5_qft_residue_controls.png new file mode 100644 index 0000000..d0abca1 Binary files /dev/null and b/outputs/fig5/fig5_qft_residue_controls.png differ diff --git a/outputs/fig6/fig6_renyi.pdf b/outputs/fig6/fig6_renyi.pdf index 88b3675..d5b26a0 100644 Binary files a/outputs/fig6/fig6_renyi.pdf and b/outputs/fig6/fig6_renyi.pdf differ diff --git a/outputs/fig6/fig6_renyi.png b/outputs/fig6/fig6_renyi.png index 471b018..599c808 100644 Binary files a/outputs/fig6/fig6_renyi.png and b/outputs/fig6/fig6_renyi.png differ diff --git a/outputs/fig7/fig7_partitions.pdf b/outputs/fig7/fig7_partitions.pdf index b8fecfa..547e07e 100644 Binary files a/outputs/fig7/fig7_partitions.pdf and b/outputs/fig7/fig7_partitions.pdf differ diff --git a/outputs/fig7/fig7_partitions.png b/outputs/fig7/fig7_partitions.png index a3bacf7..1f366ab 100644 Binary files a/outputs/fig7/fig7_partitions.png and b/outputs/fig7/fig7_partitions.png differ diff --git a/outputs/fig8/fig8_greedy_partitions.pdf b/outputs/fig8/fig8_greedy_partitions.pdf deleted file mode 100644 index 80c98a8..0000000 Binary files a/outputs/fig8/fig8_greedy_partitions.pdf and /dev/null differ diff --git a/outputs/fig8/fig8_greedy_partitions.png b/outputs/fig8/fig8_greedy_partitions.png deleted file mode 100644 index c9f6408..0000000 Binary files a/outputs/fig8/fig8_greedy_partitions.png and /dev/null differ diff --git a/outputs/fig8/fig8_samples_n10.csv b/outputs/fig8/fig8_samples_n10.csv deleted file mode 100644 index dc90509..0000000 --- a/outputs/fig8/fig8_samples_n10.csv +++ /dev/null @@ -1,10127 +0,0 @@ -n,M,family,sample,entropy 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-14,716,selected_seed_541_all_partitions,1714,6.152867988100396 -14,716,selected_seed_541_all_partitions,1715,6.1335394805027645 diff --git a/outputs/fig8/fig8_summary_n10.csv b/outputs/fig8/fig8_summary_n10.csv deleted file mode 100644 index 6a56e51..0000000 --- a/outputs/fig8/fig8_summary_n10.csv +++ /dev/null @@ -1,3 +0,0 @@ -family,n,M,seed,count,mean,std,minimum,maximum -background,10,107,20250604,10000,4.073081481098173,0.06061479547322119,3.805366359154067,4.269215927571168 -selected,10,107,163765,126,4.144912148834473,0.04551388987465532,3.9855910721337007,4.284745752538602 diff --git a/outputs/fig8/fig8_summary_n14.csv b/outputs/fig8/fig8_summary_n14.csv deleted file mode 100644 index 866542c..0000000 --- a/outputs/fig8/fig8_summary_n14.csv +++ /dev/null @@ -1,3 +0,0 @@ -family,n,M,seed,count,mean,std,minimum,maximum -background,14,716,20250605,10000,6.1431882861774705,0.01792368157844013,6.06697749743971,6.198635529561884 -selected,14,716,541,1716,6.145893791941453,0.016727229468664107,6.085708649648558,6.201464313310133 diff --git a/pyproject.toml b/pyproject.toml new file mode 100644 index 0000000..e254dd7 --- /dev/null +++ b/pyproject.toml @@ -0,0 +1,14 @@ +[project] +name = "subset-state-entanglement" +version = "1.0.0rc1" +description = "Numerical and analytical tools for support-size entanglement trajectories of random subset states" +requires-python = ">=3.10" +authors = [ + {name = "Ruge Lin"}, + {name = "Germán Sierra"}, + {name = "José I. Latorre"}, +] +dependencies = ["numpy>=1.24", "scipy>=1.10", "matplotlib>=3.7"] + +[tool.setuptools] +packages = ["subset_states"] diff --git a/requirements-tested.txt b/requirements-tested.txt new file mode 100644 index 0000000..6fed565 --- /dev/null +++ b/requirements-tested.txt @@ -0,0 +1,5 @@ +# Environment used for the publication-release validation on 2026-08-18. +Python==3.13.5 +numpy==2.3.5 +scipy==1.17.0 +matplotlib==3.10.8 diff --git a/scripts/fig1_concentration.py b/scripts/fig1_concentration.py index eddb67f..a0ab52f 100644 --- a/scripts/fig1_concentration.py +++ b/scripts/fig1_concentration.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Figure 1: concentration of random-subset entanglement over states and partitions.""" +"""Figure 1: concentration over supports and balanced bipartitions.""" from __future__ import annotations import argparse @@ -9,14 +9,11 @@ ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt import numpy as np from subset_states.core import entropy_from_support, random_balanced_partition, random_subset, summary_stats +from subset_states.csv_plotting import plot_fig1 from subset_states.experiments import m_grid, write_rows -from subset_states.plotting import apply_journal_style, make_inset_axis, save_figure def compute_curve(n: int, m_values: np.ndarray, samples: int, seed: int) -> tuple[list[dict], list[dict]]: @@ -26,7 +23,6 @@ def compute_curve(n: int, m_values: np.ndarray, samples: int, seed: int) -> tupl for m in m_values: state_values = np.empty(samples, dtype=float) partition_values = np.empty(samples, dtype=float) - fixed_support = random_subset(n, int(m), rng) for sample in range(samples): support = random_subset(n, int(m), rng) @@ -41,9 +37,7 @@ def compute_curve(n: int, m_values: np.ndarray, samples: int, seed: int) -> tupl "entropy_multiple_partitions": partition_values[sample], } ) - - st = summary_stats(state_values) - pt = summary_stats(partition_values) + st, pt = summary_stats(state_values), summary_stats(partition_values) summary_rows.append( { "m": int(m), @@ -64,37 +58,6 @@ def compute_curve(n: int, m_values: np.ndarray, samples: int, seed: int) -> tupl return summary_rows, raw_rows -def plot(summary: list[dict], zoom_summary: list[dict], out_pdf: Path, n: int) -> None: - apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.8)) - - def draw(axis, rows, markersize: float = 2.5): - m = np.array([row["m"] for row in rows]) - y_states = np.array([row["states_mean"] for row in rows]) - e_states = np.array([row["states_sem"] for row in rows]) - y_part = np.array([row["partitions_mean"] for row in rows]) - e_part = np.array([row["partitions_sem"] for row in rows]) - axis.errorbar(m, y_part, yerr=e_part, fmt="o-", markersize=markersize, capsize=1.5, label="fixed state, random partitions") - axis.errorbar(m, y_states, yerr=e_states, fmt="s--", markersize=markersize, capsize=1.5, label="fixed partition, random states") - - draw(ax, summary) - ax.set_xlabel(r"support size $M$") - ax.set_ylabel(r"entropy $S_{N,M}$") - ax.set_xlim(0, 1 << n) - ax.set_ylim(0, n / 2) - ax.legend(loc="lower center", bbox_to_anchor=(0.5, -0.38), ncol=1, frameon=False) - - inset = make_inset_axis(ax) - draw(inset, zoom_summary, markersize=2.0) - inset.set_xlim(0, max(row["m"] for row in zoom_summary) * 1.02) - inset.set_ylim(max(0, n / 2 - 3), n / 2) - inset.set_xlabel(r"$M$", labelpad=1) - inset.set_ylabel(r"$S$", labelpad=1) - inset.legend().remove() - - save_figure(fig, out_pdf) - - def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--n", type=int, default=14) @@ -106,25 +69,22 @@ def main() -> None: parser.add_argument("--seed", type=int, default=20250604) parser.add_argument("--outdir", type=Path, default=ROOT / "outputs" / "fig1") args = parser.parse_args() - args.outdir.mkdir(parents=True, exist_ok=True) N = 1 << args.n zoom_stop = min(args.zoom_stop, N) - if args.zoom_stop > N: - print(f"warning: --zoom-stop={args.zoom_stop} exceeds N=2**n={N}; using --zoom-stop={zoom_stop}.") - - m_values = m_grid(1, N, args.points, include_stop=True) - zoom_values = m_grid(1, zoom_stop, args.zoom_points, include_stop=True) - - summary, raw = compute_curve(args.n, m_values, args.samples, args.seed) - zoom_summary, zoom_raw = compute_curve(args.n, zoom_values, args.zoom_samples, args.seed + 1) - + summary, raw = compute_curve(args.n, m_grid(1, N, args.points), args.samples, args.seed) + zoom_summary, zoom_raw = compute_curve( + args.n, + m_grid(1, zoom_stop, args.zoom_points), + args.zoom_samples, + args.seed + 1, + ) fields = list(summary[0].keys()) write_rows(args.outdir / "fig1_summary.csv", summary, fields) write_rows(args.outdir / "fig1_zoom_summary.csv", zoom_summary, fields) write_rows(args.outdir / "fig1_raw.csv", raw, list(raw[0].keys())) write_rows(args.outdir / "fig1_zoom_raw.csv", zoom_raw, list(zoom_raw[0].keys())) - plot(summary, zoom_summary, args.outdir / "fig1_concentration.pdf", args.n) + plot_fig1(args.outdir, args.outdir / "fig1_concentration.pdf", n=args.n) if __name__ == "__main__": diff --git a/scripts/fig2_peak_scaling.py b/scripts/fig2_peak_scaling.py index 5515b71..bacd4c7 100644 --- a/scripts/fig2_peak_scaling.py +++ b/scripts/fig2_peak_scaling.py @@ -1,10 +1,5 @@ #!/usr/bin/env python3 -"""Figure 2: finite-size scaling of the Table-I peak values. - -This script does not rediscover the peaks. It takes the production Table-I values -as input, computes log2(M_n), the Page benchmark, and the two linear regressions -reported in the manuscript. -""" +"""Figure 2: finite-size scaling of the retained Table-I estimates.""" from __future__ import annotations import argparse @@ -14,15 +9,12 @@ ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt import numpy as np from scipy import stats from subset_states.core import exact_page_entropy_bits +from subset_states.csv_plotting import plot_fig2 from subset_states.experiments import write_rows -from subset_states.plotting import apply_journal_style, save_figure from subset_states.tables import read_table_i @@ -43,58 +35,35 @@ def fit_line(x: np.ndarray, y: np.ndarray) -> dict[str, float]: def main() -> None: parser = argparse.ArgumentParser() - parser.add_argument("--table", type=Path, default=ROOT / "data" / "table_i_peaks.csv", help="CSV with columns n,M_n,S_n") + parser.add_argument("--table", type=Path, default=ROOT / "data" / "table_i_peaks.csv") parser.add_argument("--outdir", type=Path, default=ROOT / "outputs" / "fig2") args = parser.parse_args() args.outdir.mkdir(parents=True, exist_ok=True) - rows_table = read_table_i(args.table) - n = np.asarray([row["n"] for row in rows_table], dtype=float) - M_n = np.asarray([row["M_n"] for row in rows_table], dtype=float) - S_n = np.asarray([row["S_n"] for row in rows_table], dtype=float) + table = read_table_i(args.table) + n = np.asarray([row["n"] for row in table], dtype=float) + M_n = np.asarray([row["M_n"] for row in table], dtype=float) + S_n = np.asarray([row["S_n"] for row in table], dtype=float) log2_M = np.log2(M_n) - page = np.asarray([exact_page_entropy_bits(int(x)) for x in n], dtype=float) - - fit_logM = fit_line(n, log2_M) - fit_S = fit_line(n, S_n) - - rows = [] - for ni, mi, si, logmi, pagei in zip(n, M_n, S_n, log2_M, page): - rows.append( - { - "n": int(ni), - "M_n": int(mi), - "log2_M_n": float(logmi), - "S_n": float(si), - "Page_exact_bits": float(pagei), - "Page_minus_S_n": float(pagei - si), - } - ) + page = np.asarray([exact_page_entropy_bits(int(x)) for x in n]) + rows = [ + { + "n": int(ni), + "M_n": int(mi), + "log2_M_n": float(logmi), + "S_n": float(si), + "Page_exact_bits": float(pagei), + "Page_minus_S_n": float(pagei - si), + } + for ni, mi, si, logmi, pagei in zip(n, M_n, S_n, log2_M, page) + ] write_rows(args.outdir / "fig2_table_with_page.csv", rows, rows[0].keys()) - - fit_rows = [ - {"quantity": "log2_M_n", **fit_logM}, - {"quantity": "S_n", **fit_S}, + fits = [ + {"quantity": "log2_M_n", **fit_line(n, log2_M)}, + {"quantity": "S_n", **fit_line(n, S_n)}, ] - write_rows(args.outdir / "fig2_linear_fit_summary.csv", fit_rows, fit_rows[0].keys()) - - apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.6)) - x = np.linspace(n.min() - 1, n.max() + 1, 200) - ax.plot(n, log2_M, "o", label=r"$\log_2 M_n$") - ax.plot(x, fit_logM["slope"] * x + fit_logM["intercept"], "--", linewidth=1) - ax.plot(n, S_n, "s", label=r"$S_n$") - ax.plot(x, fit_S["slope"] * x + fit_S["intercept"], "--", linewidth=1) - ax.plot(n, page, ":", label="Page average") - ax.set_xlabel(r"number of qubits $n$") - ax.set_ylabel("bits") - ax.set_xlim(n.min() - 1, n.max() + 1) - ax.set_ylim(0, max(log2_M.max(), page.max()) + 1) - ax.legend(frameon=False, loc="upper left") - save_figure(fig, args.outdir / "fig2_peak_scaling.pdf") - - print("log2(M_n) fit:", fit_logM) - print("S_n fit:", fit_S) + write_rows(args.outdir / "fig2_linear_fit_summary.csv", fits, fits[0].keys()) + plot_fig2(args.outdir, args.outdir / "fig2_peak_scaling.pdf", write_fit_summary=False) if __name__ == "__main__": diff --git a/scripts/fig3_spectral.py b/scripts/fig3_spectral.py index d537f13..467aa6d 100644 --- a/scripts/fig3_spectral.py +++ b/scripts/fig3_spectral.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Figure 3: spectrum of the reduced density matrix at peak support.""" +"""Figure 3: reduced-density-matrix bulk and isolated positive mode.""" from __future__ import annotations import argparse @@ -9,14 +9,16 @@ ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt import numpy as np -from subset_states.core import matrix_from_support, random_subset, summary_stats +from subset_states.core import ( + matrix_from_support, + mean_matrix_uniform_eigenvalue, + random_subset, + summary_stats, +) +from subset_states.csv_plotting import plot_fig3 from subset_states.experiments import write_rows -from subset_states.plotting import apply_journal_style, save_figure from subset_states.tables import PEAK_M @@ -33,15 +35,17 @@ def main() -> None: m = args.m if args.m is not None else PEAK_M[args.n] rng = np.random.default_rng(args.seed) support = random_subset(args.n, m, rng) - omega = matrix_from_support(args.n, support) - rho = omega.conj().T @ omega + matrix = matrix_from_support(args.n, support) + rho = matrix.conj().T @ matrix eigvals = np.linalg.eigvalsh(rho).real eigvals[eigvals < 1e-15] = 0.0 - eigvals = eigvals / eigvals.sum() + eigvals /= eigvals.sum() eigvals.sort() - - rows = [{"index": i, "lambda": float(lam)} for i, lam in enumerate(eigvals)] - write_rows(args.outdir / "fig3_spectrum.csv", rows, ["index", "lambda"]) + write_rows( + args.outdir / "fig3_spectrum.csv", + [{"index": i, "lambda": float(lam)} for i, lam in enumerate(eigvals)], + ["index", "lambda"], + ) lambda0 = float(eigvals[-1]) bulk = eigvals[:-1] @@ -53,6 +57,7 @@ def main() -> None: "n": args.n, "M": m, "lambda0": lambda0, + "lambda_mean_matrix": mean_matrix_uniform_eigenvalue(args.n, m), "M_over_N": m / (1 << args.n), "bulk_nonzero_count": stats.count, "bulk_mean": stats.mean, @@ -65,6 +70,7 @@ def main() -> None: "n", "M", "lambda0", + "lambda_mean_matrix", "M_over_N", "bulk_nonzero_count", "bulk_mean", @@ -73,16 +79,7 @@ def main() -> None: "bulk_max", ], ) - - apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.6)) - positive_bulk = bulk[bulk > 0] - ax.hist(positive_bulk, bins=args.bins) - ax.set_xlabel(r"eigenvalue $\lambda$ excluding $\lambda_0$") - ax.set_ylabel("count") - ax.set_xlim(0, positive_bulk.max() * 1.05) - save_figure(fig, args.outdir / "fig3_spectral_bulk.pdf") - print(f"lambda0={lambda0:.8g}, M/N={m / (1 << args.n):.8g}") + plot_fig3(args.outdir, args.outdir / "fig3_spectral_bulk.pdf", bins=args.bins) if __name__ == "__main__": diff --git a/scripts/fig4_approximation.py b/scripts/fig4_approximation.py index 257b557..64a0825 100644 --- a/scripts/fig4_approximation.py +++ b/scripts/fig4_approximation.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Figure 4: numerical entropy vs. analytical approximations D_{N,M} and T_{N,M}.""" +"""Figure 4: numerical entropy and corrected fixed-cardinality approximations.""" from __future__ import annotations import argparse @@ -9,14 +9,17 @@ ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt import numpy as np -from subset_states.core import dnm_approximation, entropy_from_support, random_subset, summary_stats, tnm_approximation +from subset_states.core import ( + dense_bulk_approximation, + entropy_from_support, + hypergeometric_occupancy_approximation, + random_subset, + summary_stats, +) +from subset_states.csv_plotting import plot_fig4 from subset_states.experiments import m_grid, write_rows -from subset_states.plotting import apply_journal_style, make_inset_axis, save_figure def compute(n: int, m_values: np.ndarray, samples: int, seed: int) -> list[dict]: @@ -25,8 +28,7 @@ def compute(n: int, m_values: np.ndarray, samples: int, seed: int) -> list[dict] for m in m_values: values = np.empty(samples, dtype=float) for sample in range(samples): - support = random_subset(n, int(m), rng) - values[sample] = entropy_from_support(n, support) + values[sample] = entropy_from_support(n, random_subset(n, int(m), rng)) stats = summary_stats(values) rows.append( { @@ -35,43 +37,13 @@ def compute(n: int, m_values: np.ndarray, samples: int, seed: int) -> list[dict] "entropy_std": stats.std, "entropy_sem": stats.sem, "entropy_count": stats.count, - "D_NM": dnm_approximation(n, int(m)), - "T_NM": tnm_approximation(n, int(m)), + "D_NM_hypergeometric": hypergeometric_occupancy_approximation(n, int(m)), + "T_NM_mean_matrix": dense_bulk_approximation(n, int(m)), } ) return rows -def draw(axis, rows, label_data: bool) -> None: - m = np.array([row["m"] for row in rows]) - mean = np.array([row["entropy_mean"] for row in rows]) - sem = np.array([row["entropy_sem"] for row in rows]) - D = np.array([row["D_NM"] for row in rows]) - T = np.array([row["T_NM"] for row in rows]) - axis.errorbar(m, mean, yerr=sem, fmt="o", markersize=2.2, capsize=1.2, label=r"numerical $S_{N,M}$" if label_data else None) - axis.plot(m, D, ":", label=r"$D_{N,M}$" if label_data else None) - axis.plot(m, T, "--", label=r"$T_{N,M}$" if label_data else None) - - -def plot(rows: list[dict], zoom_rows: list[dict], out_pdf: Path, n: int) -> None: - apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.8)) - draw(ax, rows, True) - ax.set_xlabel(r"support size $M$") - ax.set_ylabel("entropy") - ax.set_xlim(0, 1 << n) - ax.set_ylim(0, n / 2) - ax.legend(frameon=False, loc="lower center", bbox_to_anchor=(0.5, -0.35), ncol=3) - - inset = make_inset_axis(ax) - draw(inset, zoom_rows, False) - inset.set_xlim(0, max(row["m"] for row in zoom_rows) * 1.02) - inset.set_ylim(max(0, n / 2 - 3), n / 2) - inset.set_xlabel(r"$M$", labelpad=1) - inset.set_ylabel(r"$S$", labelpad=1) - save_figure(fig, out_pdf) - - def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--n", type=int, default=14) @@ -86,14 +58,16 @@ def main() -> None: args.outdir.mkdir(parents=True, exist_ok=True) N = 1 << args.n zoom_stop = min(args.zoom_stop, N) - if args.zoom_stop > N: - print(f"warning: --zoom-stop={args.zoom_stop} exceeds N=2**n={N}; using --zoom-stop={zoom_stop}.") - rows = compute(args.n, m_grid(1, N, args.points), args.samples, args.seed) - zoom_rows = compute(args.n, m_grid(1, zoom_stop, args.zoom_points), args.zoom_samples, args.seed + 1) + zoom_rows = compute( + args.n, + m_grid(1, zoom_stop, args.zoom_points), + args.zoom_samples, + args.seed + 1, + ) write_rows(args.outdir / "fig4_summary.csv", rows, rows[0].keys()) write_rows(args.outdir / "fig4_zoom_summary.csv", zoom_rows, zoom_rows[0].keys()) - plot(rows, zoom_rows, args.outdir / "fig4_approximation.pdf", args.n) + plot_fig4(args.outdir, args.outdir / "fig4_approximation.pdf", n=args.n) if __name__ == "__main__": diff --git a/scripts/fig5_qft_almost_primes.py b/scripts/fig5_qft_almost_primes.py deleted file mode 100644 index e851c42..0000000 --- a/scripts/fig5_qft_almost_primes.py +++ /dev/null @@ -1,105 +0,0 @@ -#!/usr/bin/env python3 -"""Figure 5: position/QFT entanglement and almost-prime union states.""" -from __future__ import annotations - -import argparse -from pathlib import Path -import sys - -ROOT = Path(__file__).resolve().parents[1] -sys.path.insert(0, str(ROOT)) - -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt -import numpy as np - -from subset_states.core import entropy_from_state_vector, entropy_from_support, qft_state_from_support -from subset_states.experiments import almost_prime_union_supports, m_grid, random_subset_qft_samples, write_rows -from subset_states.core import summary_stats -from subset_states.plotting import apply_journal_style, save_figure - - -def random_curve(n: int, m_values: np.ndarray, samples: int, seed: int) -> list[dict]: - rows: list[dict] = [] - for offset, m in enumerate(m_values): - position, fourier = random_subset_qft_samples(n, int(m), samples, seed=seed + offset) - pos = summary_stats(position) - qft = summary_stats(fourier) - rows.append( - { - "m": int(m), - "position_mean": pos.mean, - "position_std": pos.std, - "position_sem": pos.sem, - "qft_mean": qft.mean, - "qft_std": qft.std, - "qft_sem": qft.sem, - "delta_qft_minus_position": qft.mean - pos.mean, - } - ) - return rows - - -def almost_prime_rows(n: int) -> list[dict]: - rows: list[dict] = [] - for k, support in almost_prime_union_supports(n): - position = entropy_from_support(n, support) - qft = entropy_from_state_vector(n, qft_state_from_support(n, support)) - rows.append( - { - "k": k, - "m": int(support.size), - "position_entropy": position, - "qft_entropy": qft, - } - ) - return rows - - -def main() -> None: - parser = argparse.ArgumentParser() - parser.add_argument("--n", type=int, default=14) - parser.add_argument("--points", type=int, default=100) - parser.add_argument("--samples", type=int, default=100) - parser.add_argument("--seed", type=int, default=20250604) - parser.add_argument("--outdir", type=Path, default=ROOT / "outputs" / "fig5") - args = parser.parse_args() - args.outdir.mkdir(parents=True, exist_ok=True) - - random_rows = random_curve(args.n, m_grid(1, 1 << args.n, args.points), args.samples, args.seed) - union_rows = almost_prime_rows(args.n) - write_rows(args.outdir / "fig5_random_qft_summary.csv", random_rows, random_rows[0].keys()) - write_rows(args.outdir / "fig5_almost_prime_unions.csv", union_rows, union_rows[0].keys()) - - apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.6)) - m = np.array([row["m"] for row in random_rows]) - pos = np.array([row["position_mean"] for row in random_rows]) - pos_sem = np.array([row["position_sem"] for row in random_rows]) - qft = np.array([row["qft_mean"] for row in random_rows]) - qft_sem = np.array([row["qft_sem"] for row in random_rows]) - ax.errorbar(m, pos, yerr=pos_sem, fmt="o", markersize=2, capsize=1.2, label=r"random subset") - ax.errorbar(m, qft, yerr=qft_sem, fmt=".", markersize=2, capsize=1.2, label=r"random subset after QFT") - union_m = np.array([row["m"] for row in union_rows]) - union_pos = np.array([row["position_entropy"] for row in union_rows]) - union_qft = np.array([row["qft_entropy"] for row in union_rows]) - ax.plot(union_m, union_pos, "+", markersize=6, label=r"$U_{N,k}$") - ax.plot(union_m, union_qft, "x", markersize=5, label=r"QFT $U_{N,k}$") - ax.set_xlabel(r"support size $M$") - ax.set_ylabel("entropy") - ax.set_xlim(0, 1 << args.n) - ax.set_ylim(0, args.n / 2) - ax.legend(frameon=False, loc="lower center", bbox_to_anchor=(0.5, -0.45), ncol=2) - save_figure(fig, args.outdir / "fig5_qft_almost_primes.pdf") - - last = union_rows[-1] - print( - "Largest almost-prime union: " - f"k={last['k']}, M={last['m']} of N={1 << args.n}; " - "0 and 1 are excluded under the standard Ω(k) definition." - ) - - -if __name__ == "__main__": - main() diff --git a/scripts/fig5_qft_residue_controls.py b/scripts/fig5_qft_residue_controls.py new file mode 100644 index 0000000..8bd84df --- /dev/null +++ b/scripts/fig5_qft_residue_controls.py @@ -0,0 +1,98 @@ +#!/usr/bin/env python3 +"""Figure 5: cardinality baseline and residue-matched residual deficits.""" +from __future__ import annotations + +import argparse +import csv +from pathlib import Path +import sys + +import numpy as np + +ROOT = Path(__file__).resolve().parents[1] +sys.path.insert(0, str(ROOT)) + +import matplotlib +matplotlib.use("Agg", force=True) +import matplotlib.pyplot as plt +from matplotlib.lines import Line2D + +from subset_states.plotting import apply_journal_style, save_figure, COOL_PALETTE + + +def read_rows(path: Path) -> list[dict[str, str]]: + with path.open(newline="") as handle: + return list(csv.DictReader(handle)) + + +def values(rows: list[dict[str, str]], key: str) -> np.ndarray: + return np.asarray([float(row[key]) for row in rows], dtype=float) + + +def main() -> None: + parser = argparse.ArgumentParser() + parser.add_argument("--data-dir", type=Path, default=ROOT / "data") + parser.add_argument("--outdir", type=Path, default=ROOT / "outputs" / "fig5") + args = parser.parse_args() + args.outdir.mkdir(parents=True, exist_ok=True) + + baseline = read_rows(args.data_dir / "fig5_random_qft_summary.csv") + unions = read_rows(args.data_dir / "fig5_almost_prime_unions.csv") + controls = read_rows(args.data_dir / "residue_matched_summary.csv") + + apply_journal_style() + fig, (ax, ax2) = plt.subplots( + 1, 2, figsize=(7.25, 3.35), gridspec_kw={"width_ratios": [1.35, 1]} + ) + + m = values(baseline, "m") + position_mean = values(baseline, "position_mean") + position_std = values(baseline, "position_std") + fourier_mean = values(baseline, "qft_mean") + fourier_std = values(baseline, "qft_std") + c0, c1 = COOL_PALETTE[0], COOL_PALETTE[2] + ax.fill_between(m, position_mean - position_std, position_mean + position_std, color=c0, alpha=0.16, linewidth=0) + ax.fill_between(m, fourier_mean - fourier_std, fourier_mean + fourier_std, color=c1, alpha=0.11, linewidth=0) + ax.plot(m, position_mean, color=c0, linewidth=1.25, label="random supports") + ax.plot(m, fourier_mean, color=c1, linewidth=1.1, linestyle="--", label="random supports after QFT") + union_m = values(unions, "m") + ax.plot(union_m, values(unions, "position_entropy"), "+", color=COOL_PALETTE[3], markersize=5.8, markeredgewidth=1.1, label=r"$U_{N,k}$") + ax.plot(union_m, values(unions, "qft_entropy"), "x", color=COOL_PALETTE[5], markersize=4.8, markeredgewidth=1.0, label=r"QFT $U_{N,k}$") + ax.set_xlabel(r"support size $M$") + ax.set_ylabel("entropy (bits)") + ax.set_xlim(0, 2**14) + ax.set_ylim(0, 7) + ax.legend(frameon=False, loc="lower center", bbox_to_anchor=(0.5, -0.42), ncol=2, columnspacing=0.9, handlelength=1.8) + ax.text(0.02, 0.96, "(a)", transform=ax.transAxes, ha="left", va="top", fontweight="bold") + + labels = ["cardinality", "parity", r"mod $4$", r"mod $8$"] + x = np.arange(4, dtype=float) + colors = [COOL_PALETTE[0], COOL_PALETTE[1], COOL_PALETTE[2]] + for idx, k in enumerate((1, 2, 3)): + rows = sorted( + [row for row in controls if int(row["k"]) == k], + key=lambda row: int(row["matched_low_bits"]), + ) + position = values(rows, "position_residual_deficit") + fourier = values(rows, "fourier_residual_deficit") + ax2.plot(x, position, "o-", color=colors[idx], linewidth=1.25, markersize=4.0) + ax2.plot(x + 0.045, fourier, "o--", color=colors[idx], markerfacecolor="white", markeredgewidth=1.0, linewidth=1.0, markersize=3.8) + ax2.text(-0.03, position[0] + (0.035 if k != 2 else -0.055), rf"$k={k}$", color=colors[idx], ha="right", va="center", fontsize=8) + ax2.axhline(0, color="0.45", linewidth=0.7) + ax2.set_xticks(x, labels, rotation=22, ha="right") + ax2.set_ylabel(r"residual deficit $\Delta_t$ (bits)") + ax2.set_xlabel("constraint retained in null ensemble", labelpad=2) + ax2.set_xlim(-0.5, 3.35) + ax2.set_ylim(0, 1.62) + style_legend = [ + Line2D([0], [0], color="0.2", marker="o", linestyle="-", markersize=4, label="computational basis"), + Line2D([0], [0], color="0.2", marker="o", markerfacecolor="white", linestyle="--", markersize=4, label="after QFT"), + ] + ax2.legend(handles=style_legend, frameon=False, loc="upper right", handlelength=2.0) + ax2.text(0.02, 0.96, "(b)", transform=ax2.transAxes, ha="left", va="top", fontweight="bold") + fig.subplots_adjust(left=0.085, right=0.99, top=0.97, bottom=0.26, wspace=0.32) + save_figure(fig, args.outdir / "fig5_qft_residue_controls.pdf") + + +if __name__ == "__main__": + main() diff --git a/scripts/fig6_renyi.py b/scripts/fig6_renyi.py index 10bb189..1637079 100644 --- a/scripts/fig6_renyi.py +++ b/scripts/fig6_renyi.py @@ -9,17 +9,13 @@ ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt import numpy as np from subset_states.core import summary_stats +from subset_states.csv_plotting import plot_fig6 from subset_states.experiments import m_grid, random_subset_renyi_samples, write_rows -from subset_states.plotting import apply_journal_style, save_figure ORDERS = (1.0, 2.0, np.inf) -ORDER_LABELS = {1.0: r"$S^{(1)}$", 2.0: r"$S^{(2)}$", np.inf: r"$S^{(\infty)}$"} def compute(n: int, m_values: np.ndarray, samples: int, seed: int) -> list[dict]: @@ -43,24 +39,6 @@ def compute(n: int, m_values: np.ndarray, samples: int, seed: int) -> list[dict] return rows -def rows_for_order(rows: list[dict], order: float) -> tuple[np.ndarray, np.ndarray, np.ndarray]: - key = "inf" if np.isinf(order) else order - filtered = [row for row in rows if row["order"] == key] - return ( - np.array([row["m"] for row in filtered]), - np.array([row["mean"] for row in filtered]), - np.array([row["sem"] for row in filtered]), - ) - - -def draw(axis, rows: list[dict], *, markers: bool = True) -> None: - styles = {1.0: "o-", 2.0: "s--", np.inf: "^:"} - for order in ORDERS: - m, mean, sem = rows_for_order(rows, order) - fmt = styles[order] if markers else styles[order].replace("o", "").replace("s", "").replace("^", "") - axis.errorbar(m, mean, yerr=sem, fmt=fmt, markersize=2.2, capsize=1.2, label=ORDER_LABELS[order]) - - def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--n", type=int, default=14) @@ -75,31 +53,16 @@ def main() -> None: args.outdir.mkdir(parents=True, exist_ok=True) N = 1 << args.n zoom_stop = min(args.zoom_stop, N) - if args.zoom_stop > N: - print(f"warning: --zoom-stop={args.zoom_stop} exceeds N=2**n={N}; using --zoom-stop={zoom_stop}.") - rows = compute(args.n, m_grid(1, N, args.points), args.samples, args.seed) - zoom_rows = compute(args.n, m_grid(1, zoom_stop, args.zoom_points), args.zoom_samples, args.seed + 10_000) + zoom = compute( + args.n, + m_grid(1, zoom_stop, args.zoom_points), + args.zoom_samples, + args.seed + 10_000, + ) write_rows(args.outdir / "fig6_renyi_summary.csv", rows, rows[0].keys()) - write_rows(args.outdir / "fig6_renyi_zoom_summary.csv", zoom_rows, zoom_rows[0].keys()) - - apply_journal_style() - fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(4.7, 6.0), sharey=False) - draw(ax1, rows) - ax1.set_xlabel(r"support size $M$") - ax1.set_ylabel("Rényi entropy") - ax1.set_xlim(0, 1 << args.n) - ax1.set_ylim(0, args.n / 2) - ax1.legend(frameon=False, ncol=3, loc="lower center", bbox_to_anchor=(0.5, -0.42)) - - draw(ax2, zoom_rows) - ax2.set_xlabel(r"support size $M$") - ax2.set_ylabel("Rényi entropy") - ax2.set_xlim(0, zoom_stop) - ax2.set_ylim(max(0, args.n / 2 - 3), args.n / 2) - ax2.legend(frameon=False, ncol=3, loc="lower center", bbox_to_anchor=(0.5, -0.42)) - fig.subplots_adjust(hspace=0.55) - save_figure(fig, args.outdir / "fig6_renyi.pdf") + write_rows(args.outdir / "fig6_renyi_zoom_summary.csv", zoom, zoom[0].keys()) + plot_fig6(args.outdir, args.outdir / "fig6_renyi.pdf", n=args.n) if __name__ == "__main__": diff --git a/scripts/fig7_partitions.py b/scripts/fig7_partitions.py index ecd03bb..5e9f414 100644 --- a/scripts/fig7_partitions.py +++ b/scripts/fig7_partitions.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Figure 7: entropy over random bipartitions for subset vs. complex Haar states.""" +"""Figure 7: balanced-cut entropy distributions on one common entropy scale.""" from __future__ import annotations import argparse @@ -9,19 +9,14 @@ ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt -import numpy as np - from subset_states.core import exact_page_entropy_bits, summary_stats +from subset_states.csv_plotting import plot_fig7 from subset_states.experiments import ( complex_haar_state, partition_entropy_samples_for_fixed_subset, partition_entropy_samples_for_state, write_rows, ) -from subset_states.plotting import apply_journal_style, save_figure from subset_states.tables import PEAK_M @@ -31,6 +26,7 @@ def main() -> None: parser.add_argument("--m", type=int, default=None) parser.add_argument("--samples", type=int, default=1000) parser.add_argument("--seed", type=int, default=20250604) + parser.add_argument("--bins", type=int, default=100) parser.add_argument("--outdir", type=Path, default=ROOT / "outputs" / "fig7") args = parser.parse_args() args.outdir.mkdir(parents=True, exist_ok=True) @@ -39,62 +35,47 @@ def main() -> None: subset_values = partition_entropy_samples_for_fixed_subset(args.n, m, args.samples, seed=args.seed) haar = complex_haar_state(args.n, seed=args.seed + 1) haar_values = partition_entropy_samples_for_state(args.n, haar, args.samples, seed=args.seed + 2) - - rows = [] - for idx, value in enumerate(subset_values): - rows.append({"state_family": "subset", "sample": idx, "entropy": float(value)}) - for idx, value in enumerate(haar_values): - rows.append({"state_family": "complex_haar", "sample": idx, "entropy": float(value)}) - write_rows(args.outdir / "fig7_partition_samples.csv", rows, rows[0].keys()) - - subset_stats = summary_stats(subset_values) - haar_stats = summary_stats(haar_values) - write_rows( - args.outdir / "fig7_partition_summary.csv", - [ - { - "state_family": "subset", - "n": args.n, - "M": m, - "count": subset_stats.count, - "mean": subset_stats.mean, - "std": subset_stats.std, - "sem": subset_stats.sem, - "minimum": subset_stats.minimum, - "maximum": subset_stats.maximum, - "Page_exact_bits": exact_page_entropy_bits(args.n), - }, - { - "state_family": "complex_haar", - "n": args.n, - "M": "", - "count": haar_stats.count, - "mean": haar_stats.mean, - "std": haar_stats.std, - "sem": haar_stats.sem, - "minimum": haar_stats.minimum, - "maximum": haar_stats.maximum, - "Page_exact_bits": exact_page_entropy_bits(args.n), - }, + rows = [ + *[ + {"state_family": "subset", "sample": idx, "entropy": float(value)} + for idx, value in enumerate(subset_values) ], - ["state_family", "n", "M", "count", "mean", "std", "sem", "minimum", "maximum", "Page_exact_bits"], - ) - - apply_journal_style() - fig, axes = plt.subplots(2, 1, figsize=(4.7, 5.8)) - for ax, values, label in [ - (axes[0], subset_values, rf"subset, $M={m}$"), - (axes[1], haar_values, "complex Haar"), - ]: - ax.hist(values, bins=60) - ax.axvline(values.mean(), linestyle="--", linewidth=1, label="sample mean") - ax.axvline(exact_page_entropy_bits(args.n), linestyle=":", linewidth=1, label="Page average") - ax.set_xlabel("entropy") - ax.set_ylabel("count") - ax.set_title(label) - ax.legend(frameon=False) - fig.subplots_adjust(hspace=0.55) - save_figure(fig, args.outdir / "fig7_partitions.pdf") + *[ + {"state_family": "complex_haar", "sample": idx, "entropy": float(value)} + for idx, value in enumerate(haar_values) + ], + ] + write_rows(args.outdir / "fig7_partition_samples.csv", rows, rows[0].keys()) + subset_stats, haar_stats = summary_stats(subset_values), summary_stats(haar_values) + page = exact_page_entropy_bits(args.n) + summary_rows = [ + { + "state_family": "subset", + "n": args.n, + "M": m, + "count": subset_stats.count, + "mean": subset_stats.mean, + "std": subset_stats.std, + "sem": subset_stats.sem, + "minimum": subset_stats.minimum, + "maximum": subset_stats.maximum, + "Page_exact_bits": page, + }, + { + "state_family": "complex_haar", + "n": args.n, + "M": "", + "count": haar_stats.count, + "mean": haar_stats.mean, + "std": haar_stats.std, + "sem": haar_stats.sem, + "minimum": haar_stats.minimum, + "maximum": haar_stats.maximum, + "Page_exact_bits": page, + }, + ] + write_rows(args.outdir / "fig7_partition_summary.csv", summary_rows, summary_rows[0].keys()) + plot_fig7(args.outdir, args.outdir / "fig7_partitions.pdf", n=args.n, bins=args.bins) if __name__ == "__main__": diff --git a/scripts/fig8_greedy_partitions.py b/scripts/fig8_greedy_partitions.py deleted file mode 100644 index 157d7cc..0000000 --- a/scripts/fig8_greedy_partitions.py +++ /dev/null @@ -1,136 +0,0 @@ -#!/usr/bin/env python3 -"""Figure 8 and greedy search for high-entanglement subset samples.""" -from __future__ import annotations - -import argparse -from pathlib import Path -import sys - -ROOT = Path(__file__).resolve().parents[1] -sys.path.insert(0, str(ROOT)) - -import matplotlib -matplotlib.use("Agg", force=True) -import matplotlib.pyplot as plt -import numpy as np - -from subset_states.core import balanced_bipartitions, entropy_from_support, random_subset, summary_stats -from subset_states.experiments import random_subset_entropy_samples, write_rows -from subset_states.plotting import apply_journal_style, save_figure -from subset_states.tables import PEAK_M - - -def parse_seed_map(text: str) -> dict[int, int]: - out: dict[int, int] = {} - for item in text.split(","): - if not item.strip(): - continue - n_text, seed_text = item.split(":") - out[int(n_text)] = int(seed_text) - return out - - -def all_partition_distribution(n: int, m: int, subset_seed: int) -> np.ndarray: - support = random_subset(n, m, np.random.default_rng(subset_seed)) - partitions = list(balanced_bipartitions(n)) - values = np.empty(len(partitions), dtype=float) - for idx, right_bits in enumerate(partitions): - values[idx] = entropy_from_support(n, support, right_bits) - return values - - -def greedy_search(n: int, m: int, seed_start: int, seed_stop: int, outdir: Path) -> None: - rows = [] - best_seed = None - best_mean = -np.inf - for seed in range(seed_start, seed_stop): - values = all_partition_distribution(n, m, seed) - stats = summary_stats(values) - rows.append( - { - "seed": seed, - "n": n, - "M": m, - "partition_count": stats.count, - "mean": stats.mean, - "std": stats.std, - "minimum": stats.minimum, - "maximum": stats.maximum, - } - ) - if stats.mean > best_mean: - best_mean = stats.mean - best_seed = seed - write_rows(outdir / f"greedy_search_n{n}_{seed_start}_{seed_stop}.csv", rows, rows[0].keys()) - print(f"best seed in [{seed_start}, {seed_stop}): {best_seed}, mean={best_mean:.8f}") - - -def make_plot(n_values: list[int], seed_map: dict[int, int], background_samples: int, seed: int, outdir: Path) -> None: - apply_journal_style() - fig, axes = plt.subplots(len(n_values), 1, figsize=(4.8, 3.0 * len(n_values))) - if len(n_values) == 1: - axes = [axes] - - for panel, (ax, n) in enumerate(zip(axes, n_values)): - m = PEAK_M[n] - background = random_subset_entropy_samples(n, m, background_samples, seed=seed + panel) - selected_seed = seed_map.get(n, seed + 10_000 + panel) - selected = all_partition_distribution(n, m, selected_seed) - - raw_rows = [] - for idx, value in enumerate(background): - raw_rows.append({"n": n, "M": m, "family": "random_subsets_natural_partition", "sample": idx, "entropy": float(value)}) - for idx, value in enumerate(selected): - raw_rows.append({"n": n, "M": m, "family": f"selected_seed_{selected_seed}_all_partitions", "sample": idx, "entropy": float(value)}) - write_rows(outdir / f"fig8_samples_n{n}.csv", raw_rows, raw_rows[0].keys()) - - lo = min(background.min(), selected.min()) - hi = max(background.max(), selected.max()) - bins = np.linspace(lo, hi, 120) - ax.hist(background, bins=bins, alpha=0.65, label="random subsets, natural partition") - ax.hist(selected, bins=bins, alpha=0.65, label=f"selected subset, all partitions") - ax.axvline(background.mean(), linestyle="--", linewidth=1) - ax.axvline(selected.mean(), linestyle=":", linewidth=1) - ax.set_xlabel("entropy") - ax.set_ylabel("count") - ax.set_title(rf"$n={n}$, $M={m}$, selected seed={selected_seed}") - ax.legend(frameon=False) - - b = summary_stats(background) - s = summary_stats(selected) - write_rows( - outdir / f"fig8_summary_n{n}.csv", - [ - {"family": "background", "n": n, "M": m, "seed": seed + panel, "count": b.count, "mean": b.mean, "std": b.std, "minimum": b.minimum, "maximum": b.maximum}, - {"family": "selected", "n": n, "M": m, "seed": selected_seed, "count": s.count, "mean": s.mean, "std": s.std, "minimum": s.minimum, "maximum": s.maximum}, - ], - ["family", "n", "M", "seed", "count", "mean", "std", "minimum", "maximum"], - ) - fig.subplots_adjust(hspace=0.55) - save_figure(fig, outdir / "fig8_greedy_partitions.pdf") - - -def main() -> None: - parser = argparse.ArgumentParser() - parser.add_argument("--mode", choices=["plot", "search"], default="plot") - parser.add_argument("--n", type=int, default=10, help="n for --mode search") - parser.add_argument("--m", type=int, default=None, help="M for --mode search; defaults to Table-I peak M") - parser.add_argument("--seed-start", type=int, default=0) - parser.add_argument("--seed-stop", type=int, default=100) - parser.add_argument("--n-values", type=int, nargs="+", default=[10, 14], help="n values for --mode plot") - parser.add_argument("--best-seeds", type=str, default="10:163765,14:541") - parser.add_argument("--background-samples", type=int, default=10000) - parser.add_argument("--seed", type=int, default=20250604) - parser.add_argument("--outdir", type=Path, default=ROOT / "outputs" / "fig8") - args = parser.parse_args() - args.outdir.mkdir(parents=True, exist_ok=True) - - if args.mode == "search": - m = args.m if args.m is not None else PEAK_M[args.n] - greedy_search(args.n, m, args.seed_start, args.seed_stop, args.outdir) - else: - make_plot(args.n_values, parse_seed_map(args.best_seeds), args.background_samples, args.seed, args.outdir) - - -if __name__ == "__main__": - main() diff --git a/scripts/final_scientific_validation.py b/scripts/final_scientific_validation.py new file mode 100644 index 0000000..5d2eab9 --- /dev/null +++ b/scripts/final_scientific_validation.py @@ -0,0 +1,251 @@ +#!/usr/bin/env python3 +"""Independent checks for the final subset-state manuscript candidate.""" +from __future__ import annotations + +import csv +import math +from collections import defaultdict +from pathlib import Path + +import numpy as np +from scipy.special import digamma + +ROOT = Path(__file__).resolve().parents[1] + + +def entropy_bits(rho: np.ndarray, tol: float = 1e-14) -> float: + vals = np.linalg.eigvalsh(rho).real + vals = vals[vals > tol] + vals = vals / vals.sum() + return float(-np.sum(vals * np.log2(vals))) + + +def h_shannon(probs: np.ndarray) -> float: + p = probs[probs > 0] + return float(-np.sum(p * np.log2(p))) if p.size else 0.0 + + +def exact_mean_rho(n: int, M: int) -> np.ndarray: + d = 1 << (n // 2) + N = 1 << n + beta = (M - 1) / (d * (N - 1)) + return (1 / d - beta) * np.eye(d) + beta * np.ones((d, d)) + + +def exact_avg_purity(n: int, M: int) -> float: + d = 1 << (n // 2) + N = 1 << n + return ( + 1 / M + + 2 * (d - 1) * (M - 1) / (M * (N - 1)) + + (d - 1) ** 2 * (M - 1) * (M - 2) * (M - 3) + / (M * (N - 1) * (N - 2) * (N - 3)) + ) + + +def exhaustive_n4_checks() -> dict[str, float]: + n = 4 + N = 1 << n + d = 1 << (n // 2) + m = n // 2 + rho_sum = np.zeros((N + 1, d, d), dtype=float) + purity_sum = np.zeros(N + 1, dtype=float) + counts = np.zeros(N + 1, dtype=np.int64) + max_residue_violation = {1: -math.inf, 2: -math.inf} + max_entropy_routine_diff = 0.0 + + labels = np.arange(N, dtype=np.uint32) + batch_size = 4096 + for lo in range(1, 1 << N, batch_size): + hi = min(1 << N, lo + batch_size) + masks = np.arange(lo, hi, dtype=np.uint32) + bits = ((masks[:, None] >> labels[None, :]) & 1).astype(float) + Ms = bits.sum(axis=1).astype(np.int64) + X = bits.reshape(-1, d, d) + rho = np.einsum('bai,baj->bij', X, X) / Ms[:, None, None] + evals = np.linalg.eigvalsh(rho).real + positive = np.where(evals > 1e-14, evals, 1.0) + entropy = -np.sum(np.where(evals > 1e-14, evals * np.log2(positive), 0.0), axis=1) + if lo == 1: + entropy_direct = np.asarray([entropy_bits(r) for r in rho[:128]]) + max_entropy_routine_diff = max( + max_entropy_routine_diff, + float(np.max(np.abs(entropy[:128] - entropy_direct))), + ) + purity = np.sum(evals * evals, axis=1) + + np.add.at(rho_sum, Ms, rho) + purity_sum += np.bincount(Ms, weights=purity, minlength=N + 1) + counts += np.bincount(Ms, minlength=N + 1) + + for t in (1, 2): + modulus = 1 << t + residue_counts = np.stack( + [bits[:, (labels % modulus) == r].sum(axis=1) for r in range(modulus)], + axis=1, + ) + probs = residue_counts / Ms[:, None] + p_safe = np.where(probs > 0, probs, 1.0) + H = -np.sum(np.where(probs > 0, probs * np.log2(p_safe), 0.0), axis=1) + bound = m - t + H + max_residue_violation[t] = max( + max_residue_violation[t], + float(np.max(entropy - bound)), + ) + + max_mean_rho_error = 0.0 + max_purity_error = 0.0 + for M in range(1, N + 1): + empirical_rho = rho_sum[M] / counts[M] + empirical_purity = purity_sum[M] / counts[M] + max_mean_rho_error = max( + max_mean_rho_error, + float(np.max(np.abs(empirical_rho - exact_mean_rho(n, M)))), + ) + max_purity_error = max( + max_purity_error, + abs(empirical_purity - exact_avg_purity(n, M)), + ) + + return { + "supports_enumerated": float((1 << N) - 1), + "max_mean_rho_error": max_mean_rho_error, + "max_average_purity_error": max_purity_error, + "max_residue_bound_violation_t1": max_residue_violation[1], + "max_residue_bound_violation_t2": max_residue_violation[2], + "max_entropy_routine_difference": max_entropy_routine_diff, + } + +def page_entropy(n: int) -> float: + d = 1 << (n // 2) + return float((digamma(d * d + 1) - digamma(d + 1) - (d - 1) / (2 * d)) / math.log(2)) + + +def table_fit_checks() -> dict[str, float]: + rows = np.asarray( + [ + (10, 107, 4.072), + (12, 276, 5.108), + (14, 716, 6.143), + (16, 1873, 7.176), + (18, 4934, 8.196), + (20, 13091, 9.215), + (22, 34771, 10.231), + (24, 93018, 11.242), + (26, 250660, 12.251), + (28, 672556, 13.258), + (30, 1836685, 14.263), + ], + dtype=float, + ) + n, M, S = rows.T + slope_S, intercept_S = np.polyfit(n, S, 1) + slope_M, intercept_M = np.polyfit(n, np.log2(M), 1) + page = np.asarray([page_entropy(int(x)) for x in n]) + gaps = page - S + fractions = M / np.power(2.0, n) + assert np.all(np.diff(gaps) < 0), "Page gaps are not strictly decreasing" + assert np.all(np.diff(fractions) < 0), "support fractions are not strictly decreasing" + return { + "S_slope": float(slope_S), + "S_intercept": float(intercept_S), + "log2M_slope": float(slope_M), + "log2M_intercept": float(intercept_M), + "page_gap_n10": float(gaps[0]), + "page_gap_n30": float(gaps[-1]), + "support_fraction_n10": float(fractions[0]), + "support_fraction_n30": float(fractions[-1]), + } + + +def dense_ansatz_equivalence() -> float: + n = 14 + N = 1 << n + d = 1 << (n // 2) + max_diff = 0.0 + for M in range(1, N): + lam = 1 / d + (d - 1) * (M - 1) / (d * (N - 1)) + old = ( + (1 - lam) * (math.log(d) - math.log(1 - lam) - 0.5) + - lam * math.log(lam) + ) / math.log(2) + h2 = -lam * math.log2(lam) - (1 - lam) * math.log2(1 - lam) + new = h2 + (1 - lam) * (math.log2(d) - 1 / (2 * math.log(2))) + max_diff = max(max_diff, abs(old - new)) + return max_diff + + +def residue_checks() -> dict[str, float]: + path = ROOT / "data" / "residue_matched_summary.csv" + with path.open(newline="") as f: + rows = list(csv.DictReader(f)) + + by_key = {(int(r["k"]), int(r["matched_low_bits"])): r for r in rows} + strongest = [(1, 1), (2, 2), (3, 3)] + expected = { + (1, 1): (0.124881, 0.114442, 0.885607, 0.894136), + (2, 2): (0.230201, 0.212232, 0.841422, 0.851975), + (3, 3): (0.111500, 0.103991, 0.910577, 0.916102), + } + max_claim_error = 0.0 + for key in strongest: + r = by_key[key] + vals = ( + float(r["position_residual_deficit"]), + float(r["fourier_residual_deficit"]), + float(r["cardinality_deficit_reduction_position"]), + float(r["cardinality_deficit_reduction_fourier"]), + ) + max_claim_error = max(max_claim_error, max(abs(a - b) for a, b in zip(vals, expected[key]))) + assert int(r["position_null_count_at_or_below_structured"]) == 0 + assert int(r["fourier_null_count_at_or_below_structured"]) == 0 + + prime = by_key[(1, 1)] + forced_gap = float(prime["forced_gap_from_balanced_max_bits"]) + ceiling = float(prime["entropy_ceiling_bits"]) + return { + "max_residue_claim_rounding_error": max_claim_error, + "prime_parity_ceiling_bits": ceiling, + "prime_forced_gap_bits": forced_gap, + "all_six_strongest_controls_below_all_1000_nulls": 1.0, + } + + +def main() -> None: + results = { + "exhaustive_n4": exhaustive_n4_checks(), + "table_fits": table_fit_checks(), + "dense_ansatz": {"max_old_new_difference": dense_ansatz_equivalence()}, + "residue_controls": residue_checks(), + } + + lines = ["FINAL SCIENTIFIC VALIDATION", "=" * 29, ""] + for section, values in results.items(): + lines.append(section) + lines.append("-" * len(section)) + for key, value in values.items(): + lines.append(f"{key}: {value:.16g}") + lines.append("") + + # Hard acceptance thresholds. + ex = results["exhaustive_n4"] + assert ex["max_mean_rho_error"] < 5e-13 + assert ex["max_average_purity_error"] < 5e-13 + assert ex["max_residue_bound_violation_t1"] < 5e-13 + assert ex["max_residue_bound_violation_t2"] < 5e-13 + assert results["dense_ansatz"]["max_old_new_difference"] < 5e-13 + tf = results["table_fits"] + assert abs(tf["S_slope"] - 0.5093) < 1e-12 + assert abs(tf["S_intercept"] + 0.9900909090909096) < 1e-12 + assert abs(tf["log2M_slope"] - 0.7035409513877945) < 1e-12 + assert abs(tf["log2M_intercept"] + 0.35773436814817394) < 1e-12 + + lines.append("STATUS: PASS") + out = ROOT / "validation" / "FINAL_SCIENTIFIC_VALIDATION.txt" + out.parent.mkdir(parents=True, exist_ok=True) + out.write_text("\n".join(lines) + "\n") + print(out.read_text()) + + +if __name__ == "__main__": + main() diff --git a/scripts/peak_scaling_verification.py b/scripts/peak_scaling_verification.py index 9236249..254e98b 100644 --- a/scripts/peak_scaling_verification.py +++ b/scripts/peak_scaling_verification.py @@ -1,13 +1,9 @@ #!/usr/bin/env python3 -"""Local verification of the Table-I peak scaling values. +"""Local verification of the retained Table-I peak values. -This script is deliberately local. It does not perform a global search over all -support sizes. Instead, for each selected n it samples random subset states in a -window centered at the tabulated peak M_n, fits a quadratic in log2(M), and -reports whether the fitted local maximum is consistent with the table. - -The workload is controlled by data/peak_verification_schedule.csv or by command -line overrides such as --samples, --points and --span. +This is a neighbourhood check, not a reconstruction of the historical global +search. It samples support sizes near each recorded peak and fits a quadratic +in log2(M). """ from __future__ import annotations @@ -15,7 +11,8 @@ import csv from pathlib import Path import sys -from typing import Iterable + +import numpy as np ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) @@ -23,7 +20,6 @@ import matplotlib matplotlib.use("Agg", force=True) import matplotlib.pyplot as plt -import numpy as np from subset_states.core import summary_stats from subset_states.experiments import random_subset_entropy_samples, write_rows @@ -32,230 +28,112 @@ from subset_states.tables import read_table_i, select_table_rows -def read_schedule(path: Path | None) -> dict[int, dict[str, float | int]]: - if path is None: - return {} +def read_schedule(path: Path) -> dict[int, dict[str, float | int]]: with path.open(newline="") as handle: lines = [line for line in handle if line.strip() and not line.lstrip().startswith("#")] - if not lines: - return {} reader = csv.DictReader(lines) - required = {"n", "samples", "points"} - missing = required - set(reader.fieldnames or []) - if missing: - raise ValueError(f"{path} is missing required columns: {sorted(missing)}") - - schedule: dict[int, dict[str, float | int]] = {} - for row in reader: - n = int(row["n"]) - schedule[n] = { + return { + int(row["n"]): { "samples": int(row["samples"]), "points": int(row["points"]), - "span": float(row.get("span", 0.25) or 0.25), + "span": float(row["span"]), } - if row.get("half_width") not in (None, ""): - schedule[n]["half_width"] = int(row["half_width"]) - return schedule - - -def selected_n_values(args: argparse.Namespace, table_rows: list[dict[str, int | float]]) -> list[int]: - table_n = [int(row["n"]) for row in table_rows] - if args.all_table: - return table_n - if args.n_values: - return [int(n) for n in args.n_values] - return [n for n in table_n if n <= args.default_max_n] - - -def row_parameters(n: int, schedule: dict[int, dict[str, float | int]], args: argparse.Namespace) -> tuple[int, int, float, int | None]: - row = schedule.get(n, {}) - samples = int(args.samples if args.samples is not None else row.get("samples", 50)) - points = int(args.points if args.points is not None else row.get("points", 15)) - span = float(args.span if args.span is not None else row.get("span", 0.25)) - half_width = args.half_width if args.half_width is not None else row.get("half_width") - half_width_int = None if half_width is None else int(half_width) - return samples, points, span, half_width_int + for row in reader + } -def run_one( - *, - n: int, - table_m: int, - table_s: float, - samples: int, - points: int, - span: float, - half_width: int | None, - seed: int, - outdir: Path, - label: str, -) -> dict: - m_values = local_m_grid(n, table_m, points=points, span=span, half_width=half_width) - rows: list[dict] = [] - - for offset, m in enumerate(m_values): - values = random_subset_entropy_samples(n, int(m), samples, seed=seed + offset) - stats = summary_stats(values) - rows.append( - { - "n": n, - "m": int(m), - "log2_m": float(np.log2(m)), - "table_M_n": table_m, - "table_S_n": table_s, - "delta_m_from_table": int(m - table_m), - "count": stats.count, - "mean": stats.mean, - "std": stats.std, - "sem": stats.sem, - "minimum": stats.minimum, - "maximum": stats.maximum, - } - ) - - suffix = f"_{label}" if label else "" - sample_path = outdir / f"peak_verification_n{n}{suffix}_samples.csv" - write_rows(sample_path, rows, rows[0].keys()) - - m = np.asarray([row["m"] for row in rows], dtype=float) - mean = np.asarray([row["mean"] for row in rows], dtype=float) - sem = np.asarray([row["sem"] for row in rows], dtype=float) - fit = quadratic_peak_fit(m, mean, sem) - fit.update( - { - "n": n, - "table_M_n": table_m, - "table_S_n": table_s, - "M_peak_minus_table_M_n": float(fit["M_peak"] - table_m), - "S_peak_minus_table_S_n": float(fit["S_peak"] - table_s), - "window_low": int(m.min()), - "window_high": int(m.max()), - "points_requested": points, - "points_used": int(m.size), - "samples_per_m": samples, - "span": span, - "half_width": "" if half_width is None else half_width, - "seed": seed, - "sample_csv": sample_path.name, - } - ) - fit_path = outdir / f"peak_verification_n{n}{suffix}_fit.csv" - write_rows(fit_path, [fit], fit.keys()) - - make_one_plot(n=n, rows=rows, fit=fit, out_pdf=outdir / f"peak_verification_n{n}{suffix}.pdf") - return fit - - -def make_one_plot(*, n: int, rows: list[dict], fit: dict, out_pdf: Path) -> None: +def plot_one(n: int, rows: list[dict], fit: dict, out_pdf: Path) -> None: apply_journal_style() fig, ax = plt.subplots(figsize=(4.7, 3.6)) - m = np.asarray([row["m"] for row in rows], dtype=float) x = np.log2(m) mean = np.asarray([row["mean"] for row in rows], dtype=float) sem = np.asarray([row["sem"] for row in rows], dtype=float) - ax.errorbar(x, mean, yerr=sem, fmt="o", markersize=3, capsize=1.5, label="sampled mean") - x_fit = np.linspace(x.min(), x.max(), 300) - y_fit = fit["quadratic_a"] * x_fit**2 + fit["quadratic_b"] * x_fit + fit["quadratic_c"] - ax.plot(x_fit, y_fit, "--", linewidth=1, label="quadratic fit") + xx = np.linspace(x.min(), x.max(), 300) + yy = fit["quadratic_a"] * xx**2 + fit["quadratic_b"] * xx + fit["quadratic_c"] + ax.plot(xx, yy, "--", linewidth=1, label="quadratic fit") ax.axvline(np.log2(float(fit["table_M_n"])), linestyle=":", linewidth=1, label=r"Table $M_n$") ax.axvline(float(fit["log2_M_peak"]), linestyle="-.", linewidth=1, label="fit maximum") - ax.axhline(float(fit["table_S_n"]), linestyle=":", linewidth=0.8) ax.set_xlabel(r"$\log_2 M$") ax.set_ylabel(r"$S_{N,M}$") ax.set_title(fr"local peak check, $n={n}$") - ax.legend(frameon=False, loc="best") - save_figure(fig, out_pdf) - - -def make_summary_plot(fit_rows: Iterable[dict], out_pdf: Path) -> None: - rows = list(fit_rows) - if not rows: - return - apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.6)) - n = np.asarray([float(row["n"]) for row in rows]) - delta_m = np.asarray([float(row["M_peak_minus_table_M_n"]) for row in rows]) - delta_s = np.asarray([float(row["S_peak_minus_table_S_n"]) for row in rows]) - ax.axhline(0.0, linestyle=":", linewidth=1) - ax.plot(n, delta_s, "o-", label=r"$S_{\rm fit}-S_n$ (bits)") - ax.set_xlabel(r"number of qubits $n$") - ax.set_ylabel(r"entropy difference") - ax2 = ax.twinx() - ax2.plot(n, delta_m, "s--", label=r"$M_{\rm fit}-M_n$") - ax2.set_ylabel(r"support-size difference") - handles, labels = ax.get_legend_handles_labels() - handles2, labels2 = ax2.get_legend_handles_labels() - ax.legend(handles + handles2, labels + labels2, frameon=False, loc="best") + ax.legend(frameon=False) save_figure(fig, out_pdf) def main() -> None: parser = argparse.ArgumentParser() - parser.add_argument("--table", type=Path, default=ROOT / "data" / "table_i_peaks.csv", help="CSV with columns n,M_n,S_n") - parser.add_argument("--schedule", type=Path, default=ROOT / "data" / "peak_verification_schedule.csv", help="CSV with columns n,samples,points,span") - parser.add_argument("--n-values", type=int, nargs="+", default=None, help="n values to verify, e.g. --n-values 10 12 14") - parser.add_argument("--all-table", action="store_true", help="verify all n values in the table; can be expensive") - parser.add_argument("--default-max-n", type=int, default=20, help="default n cutoff when neither --n-values nor --all-table is used") - parser.add_argument("--samples", type=int, default=None, help="override samples per M for all selected n") - parser.add_argument("--points", type=int, default=None, help="override number of M grid points for all selected n") - parser.add_argument("--span", type=float, default=None, help="override fractional half-width around table M_n") - parser.add_argument("--half-width", type=int, default=None, help="override span with an absolute half-width around table M_n") + parser.add_argument("--table", type=Path, default=ROOT / "data" / "table_i_peaks.csv") + parser.add_argument("--schedule", type=Path, default=ROOT / "data" / "peak_verification_schedule.csv") + parser.add_argument("--n-values", type=int, nargs="+", default=None) + parser.add_argument("--all-table", action="store_true") + parser.add_argument("--default-max-n", type=int, default=20) + parser.add_argument("--samples", type=int, default=None) + parser.add_argument("--points", type=int, default=None) + parser.add_argument("--span", type=float, default=None) parser.add_argument("--seed", type=int, default=20250605) - parser.add_argument("--label", type=str, default="", help="optional suffix for output files") + parser.add_argument("--dry-run", action="store_true") parser.add_argument("--outdir", type=Path, default=ROOT / "outputs" / "peak_verification") - parser.add_argument("--dry-run", action="store_true", help="print selected jobs without sampling") args = parser.parse_args() - args.outdir.mkdir(parents=True, exist_ok=True) - table_rows_all = read_table_i(args.table) - n_values = selected_n_values(args, table_rows_all) - table_rows = select_table_rows(table_rows_all, n_values) + table = read_table_i(args.table) + if args.all_table: + n_values = [int(row["n"]) for row in table] + elif args.n_values: + n_values = args.n_values + else: + n_values = [int(row["n"]) for row in table if int(row["n"]) <= args.default_max_n] + selected = select_table_rows(table, n_values) schedule = read_schedule(args.schedule) + args.outdir.mkdir(parents=True, exist_ok=True) - print("Local peak-verification jobs:") jobs = [] - for index, row in enumerate(table_rows): + for index, row in enumerate(selected): n = int(row["n"]) - table_m = int(row["M_n"]) - table_s = float(row["S_n"]) - samples, points, span, half_width = row_parameters(n, schedule, args) - seed = args.seed + 10000 * index - jobs.append((n, table_m, table_s, samples, points, span, half_width, seed)) - width = f"half_width={half_width}" if half_width is not None else f"span={span:g}" - print(f" n={n:2d}, table M_n={table_m}, samples={samples}, points={points}, {width}, seed={seed}") - + config = schedule.get(n, {"samples": 50, "points": 15, "span": 0.25}) + jobs.append( + { + "n": n, + "table_M_n": int(row["M_n"]), + "table_S_n": float(row["S_n"]), + "samples": args.samples or int(config["samples"]), + "points": args.points or int(config["points"]), + "span": args.span if args.span is not None else float(config["span"]), + "seed": args.seed + 10000 * index, + } + ) + for job in jobs: + print(job) if args.dry_run: return - fit_rows = [] - for n, table_m, table_s, samples, points, span, half_width, seed in jobs: - fit_rows.append( - run_one( - n=n, - table_m=table_m, - table_s=table_s, - samples=samples, - points=points, - span=span, - half_width=half_width, - seed=seed, - outdir=args.outdir, - label=args.label, - ) + summary = [] + for job in jobs: + grid = local_m_grid(job["n"], job["table_M_n"], points=job["points"], span=job["span"]) + rows = [] + for offset, m in enumerate(grid): + vals = random_subset_entropy_samples(job["n"], int(m), job["samples"], seed=job["seed"] + offset) + stats = summary_stats(vals) + rows.append({ + "n": job["n"], "m": int(m), "log2_m": float(np.log2(m)), + "table_M_n": job["table_M_n"], "table_S_n": job["table_S_n"], + "count": stats.count, "mean": stats.mean, "std": stats.std, + "sem": stats.sem, "minimum": stats.minimum, "maximum": stats.maximum, + }) + fit = quadratic_peak_fit( + np.asarray([row["m"] for row in rows]), + np.asarray([row["mean"] for row in rows]), + np.asarray([row["sem"] for row in rows]), ) - print( - f"n={n:2d}: M_fit={fit_rows[-1]['M_peak']:.3f}, " - f"S_fit={fit_rows[-1]['S_peak']:.6f}, " - f"status={fit_rows[-1]['fit_status']}" - ) - - suffix = f"_{args.label}" if args.label else "" - summary_path = args.outdir / f"peak_verification_summary{suffix}.csv" - write_rows(summary_path, fit_rows, fit_rows[0].keys()) - make_summary_plot(fit_rows, args.outdir / f"peak_verification_summary{suffix}.pdf") - print("written:", summary_path) + fit.update(job) + fit["M_peak_minus_table_M_n"] = float(fit["M_peak"] - job["table_M_n"]) + fit["S_peak_minus_table_S_n"] = float(fit["S_peak"] - job["table_S_n"]) + write_rows(args.outdir / f"peak_verification_n{job['n']}_samples.csv", rows, rows[0].keys()) + write_rows(args.outdir / f"peak_verification_n{job['n']}_fit.csv", [fit], fit.keys()) + plot_one(job["n"], rows, fit, args.outdir / f"peak_verification_n{job['n']}.pdf") + summary.append(fit) + write_rows(args.outdir / "peak_verification_summary.csv", summary, summary[0].keys()) if __name__ == "__main__": diff --git a/scripts/plot_fig1_from_csv.py b/scripts/plot_fig1_from_csv.py index 6730e4e..c461f68 100644 --- a/scripts/plot_fig1_from_csv.py +++ b/scripts/plot_fig1_from_csv.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Redraw Figure 1 from previously generated CSV files.""" +"""Redraw revised Figure 1 from existing CSV files.""" from __future__ import annotations import argparse @@ -16,10 +16,9 @@ def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "fig1") parser.add_argument("--out", type=Path, default=None) - parser.add_argument("--n", type=int, default=None, help="Optional; inferred from fig1_summary.csv if omitted.") args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig1_concentration_from_csv.pdf" - plot_fig1(args.data_dir, out, n=args.n) + out = args.out if args.out is not None else args.data_dir / "fig1_concentration.pdf" + plot_fig1(args.data_dir, out) if __name__ == "__main__": diff --git a/scripts/plot_fig2_from_csv.py b/scripts/plot_fig2_from_csv.py index 91e061d..d8c2d61 100644 --- a/scripts/plot_fig2_from_csv.py +++ b/scripts/plot_fig2_from_csv.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Redraw Figure 2 from fig2_table_with_page.csv.""" +"""Redraw revised Figure 2 from existing CSV files.""" from __future__ import annotations import argparse @@ -17,7 +17,7 @@ def main() -> None: parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "fig2") parser.add_argument("--out", type=Path, default=None) args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig2_peak_scaling_from_csv.pdf" + out = args.out if args.out is not None else args.data_dir / "fig2_peak_scaling.pdf" plot_fig2(args.data_dir, out) diff --git a/scripts/plot_fig3_from_csv.py b/scripts/plot_fig3_from_csv.py index 5ad9b2c..bcbec5d 100644 --- a/scripts/plot_fig3_from_csv.py +++ b/scripts/plot_fig3_from_csv.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Redraw Figure 3 from fig3_spectrum.csv.""" +"""Redraw revised Figure 3 from existing CSV files.""" from __future__ import annotations import argparse @@ -18,7 +18,7 @@ def main() -> None: parser.add_argument("--out", type=Path, default=None) parser.add_argument("--bins", type=int, default=500) args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig3_spectral_bulk_from_csv.pdf" + out = args.out if args.out is not None else args.data_dir / "fig3_spectral_bulk.pdf" plot_fig3(args.data_dir, out, bins=args.bins) diff --git a/scripts/plot_fig4_from_csv.py b/scripts/plot_fig4_from_csv.py index 41ff470..7954de5 100644 --- a/scripts/plot_fig4_from_csv.py +++ b/scripts/plot_fig4_from_csv.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Redraw Figure 4 from previously generated CSV files.""" +"""Redraw revised Figure 4 from existing CSV files.""" from __future__ import annotations import argparse @@ -16,10 +16,9 @@ def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "fig4") parser.add_argument("--out", type=Path, default=None) - parser.add_argument("--n", type=int, default=None, help="Optional; inferred from fig4_summary.csv if omitted.") args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig4_approximation_from_csv.pdf" - plot_fig4(args.data_dir, out, n=args.n) + out = args.out if args.out is not None else args.data_dir / "fig4_approximation.pdf" + plot_fig4(args.data_dir, out) if __name__ == "__main__": diff --git a/scripts/plot_fig5_from_csv.py b/scripts/plot_fig5_from_csv.py deleted file mode 100644 index 8d5279b..0000000 --- a/scripts/plot_fig5_from_csv.py +++ /dev/null @@ -1,26 +0,0 @@ -#!/usr/bin/env python3 -"""Redraw Figure 5 from previously generated CSV files.""" -from __future__ import annotations - -import argparse -from pathlib import Path -import sys - -ROOT = Path(__file__).resolve().parents[1] -sys.path.insert(0, str(ROOT)) - -from subset_states.csv_plotting import plot_fig5 - - -def main() -> None: - parser = argparse.ArgumentParser() - parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "fig5") - parser.add_argument("--out", type=Path, default=None) - parser.add_argument("--n", type=int, default=None, help="Optional; inferred from fig5_random_qft_summary.csv if omitted.") - args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig5_qft_almost_primes_from_csv.pdf" - plot_fig5(args.data_dir, out, n=args.n) - - -if __name__ == "__main__": - main() diff --git a/scripts/plot_fig6_from_csv.py b/scripts/plot_fig6_from_csv.py index fdd3d21..937bf50 100644 --- a/scripts/plot_fig6_from_csv.py +++ b/scripts/plot_fig6_from_csv.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Redraw Figure 6 from previously generated CSV files.""" +"""Redraw revised Figure 6 from existing CSV files.""" from __future__ import annotations import argparse @@ -16,10 +16,9 @@ def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "fig6") parser.add_argument("--out", type=Path, default=None) - parser.add_argument("--n", type=int, default=None, help="Optional; inferred from fig6_renyi_summary.csv if omitted.") args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig6_renyi_from_csv.pdf" - plot_fig6(args.data_dir, out, n=args.n) + out = args.out if args.out is not None else args.data_dir / "fig6_renyi.pdf" + plot_fig6(args.data_dir, out) if __name__ == "__main__": diff --git a/scripts/plot_fig7_from_csv.py b/scripts/plot_fig7_from_csv.py index 8a24920..2124011 100644 --- a/scripts/plot_fig7_from_csv.py +++ b/scripts/plot_fig7_from_csv.py @@ -1,5 +1,5 @@ #!/usr/bin/env python3 -"""Redraw Figure 7 from fig7_partition_samples.csv.""" +"""Redraw revised Figure 7 from existing CSV files.""" from __future__ import annotations import argparse @@ -16,11 +16,10 @@ def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "fig7") parser.add_argument("--out", type=Path, default=None) - parser.add_argument("--n", type=int, default=None) - parser.add_argument("--bins", type=int, default=60) + parser.add_argument("--bins", type=int, default=100) args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig7_partitions_from_csv.pdf" - plot_fig7(args.data_dir, out, n=args.n, bins=args.bins) + out = args.out if args.out is not None else args.data_dir / "fig7_partitions.pdf" + plot_fig7(args.data_dir, out, bins=args.bins) if __name__ == "__main__": diff --git a/scripts/plot_fig8_from_csv.py b/scripts/plot_fig8_from_csv.py deleted file mode 100644 index f92eef6..0000000 --- a/scripts/plot_fig8_from_csv.py +++ /dev/null @@ -1,27 +0,0 @@ -#!/usr/bin/env python3 -"""Redraw Figure 8 from fig8_samples_n*.csv.""" -from __future__ import annotations - -import argparse -from pathlib import Path -import sys - -ROOT = Path(__file__).resolve().parents[1] -sys.path.insert(0, str(ROOT)) - -from subset_states.csv_plotting import plot_fig8 - - -def main() -> None: - parser = argparse.ArgumentParser() - parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "fig8") - parser.add_argument("--out", type=Path, default=None) - parser.add_argument("--n-values", type=int, nargs="*", default=None) - parser.add_argument("--bins", type=int, default=120) - args = parser.parse_args() - out = args.out if args.out is not None else args.data_dir / "fig8_greedy_partitions_from_csv.pdf" - plot_fig8(args.data_dir, out, n_values=args.n_values, bins=args.bins) - - -if __name__ == "__main__": - main() diff --git a/scripts/plot_peak_verification_from_csv.py b/scripts/plot_peak_verification_from_csv.py index b226608..36cc614 100644 --- a/scripts/plot_peak_verification_from_csv.py +++ b/scripts/plot_peak_verification_from_csv.py @@ -1,30 +1,23 @@ #!/usr/bin/env python3 -"""Redraw a local peak-verification plot from CSV files.""" +"""Redraw one local peak-verification plot from released CSV files.""" from __future__ import annotations - import argparse from pathlib import Path import sys - ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) - from subset_states.csv_plotting import plot_peak_search - def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--n", type=int, required=True) - parser.add_argument("--label", type=str, default="") parser.add_argument("--data-dir", type=Path, default=ROOT / "outputs" / "peak_verification") parser.add_argument("--out", type=Path, default=None) args = parser.parse_args() - suffix = f"_{args.label}" if args.label else "" - samples = args.data_dir / f"peak_verification_n{args.n}{suffix}_samples.csv" - fit = args.data_dir / f"peak_verification_n{args.n}{suffix}_fit.csv" - out = args.out or (args.data_dir / f"peak_verification_n{args.n}{suffix}_from_csv.pdf") + samples = args.data_dir / f"peak_verification_n{args.n}_samples.csv" + fit = args.data_dir / f"peak_verification_n{args.n}_fit.csv" + out = args.out or args.data_dir / f"peak_verification_n{args.n}_from_csv.pdf" plot_peak_search(samples, fit, out) - if __name__ == "__main__": main() diff --git a/scripts/regenerate_fig5_baseline.py b/scripts/regenerate_fig5_baseline.py new file mode 100644 index 0000000..3d7986c --- /dev/null +++ b/scripts/regenerate_fig5_baseline.py @@ -0,0 +1,29 @@ +#!/usr/bin/env python3 +"""Regenerate the n=14 random position/Fourier baseline and arithmetic points.""" +from __future__ import annotations +import argparse, csv, sys +from pathlib import Path +import numpy as np +ROOT=Path(__file__).resolve().parents[1] +sys.path.insert(0,str(ROOT)) +from subset_states.core import entropy_from_state_vector, entropy_from_support, qft_state_from_support, summary_stats +from subset_states.experiments import almost_prime_union_supports, m_grid, random_subset_qft_samples + +def write(path, rows): + path.parent.mkdir(parents=True,exist_ok=True) + with path.open('w',newline='') as f: + w=csv.DictWriter(f,fieldnames=list(rows[0].keys()));w.writeheader();w.writerows(rows) + +def main(): + p=argparse.ArgumentParser();p.add_argument('--n',type=int,default=14);p.add_argument('--points',type=int,default=100);p.add_argument('--samples',type=int,default=100);p.add_argument('--seed',type=int,default=20250604);p.add_argument('--outdir',type=Path,default=ROOT/'data');a=p.parse_args() + rows=[] + for off,m in enumerate(m_grid(1,1< None: + command = [sys.executable, str(ROOT / "scripts" / script), *args] + print("+", " ".join(command)) + subprocess.run(command, check=True, cwd=ROOT) + + +def main() -> None: + parser = argparse.ArgumentParser() + parser.add_argument("--full", action="store_true", help="run every publication computation; expensive") + parser.add_argument("--smoke", action="store_true", help="run reduced-size computation checks") + args = parser.parse_args() + + if args.full: + for script in [ + "fig1_concentration.py", "fig2_peak_scaling.py", "fig3_spectral.py", + "fig4_approximation.py", "regenerate_fig5_baseline.py", + "run_residue_controls.py", "fig5_qft_residue_controls.py", + "fig6_renyi.py", "fig7_partitions.py", + ]: + run(script) + elif args.smoke: + run("fig1_concentration.py", "--n", "6", "--points", "5", "--samples", "2", "--zoom-points", "4", "--zoom-samples", "2", "--zoom-stop", "32", "--outdir", str(ROOT / "outputs" / "smoke" / "fig1")) + run("fig2_peak_scaling.py") + run("fig3_spectral.py", "--n", "8", "--m", "40", "--bins", "20", "--outdir", str(ROOT / "outputs" / "smoke" / "fig3")) + run("fig4_approximation.py", "--n", "6", "--points", "5", "--samples", "2", "--zoom-stop", "32", "--zoom-points", "4", "--zoom-samples", "2", "--outdir", str(ROOT / "outputs" / "smoke" / "fig4")) + run("fig5_qft_residue_controls.py") + run("fig6_renyi.py", "--n", "6", "--points", "5", "--samples", "2", "--zoom-stop", "32", "--zoom-points", "4", "--zoom-samples", "2", "--outdir", str(ROOT / "outputs" / "smoke" / "fig6")) + run("fig7_partitions.py", "--n", "6", "--m", "20", "--samples", "3", "--outdir", str(ROOT / "outputs" / "smoke" / "fig7")) + else: + run("fig2_peak_scaling.py") + run("fig5_qft_residue_controls.py") + + missing = [str(ROOT / "outputs" / rel) for rel in FIGURE_FILES.values() if not (ROOT / "outputs" / rel).exists()] + if missing: + raise SystemExit("missing released figure files:\n" + "\n".join(missing)) + print("All seven released figure PDFs are present.") + + +if __name__ == "__main__": + main() diff --git a/scripts/run_residue_controls.py b/scripts/run_residue_controls.py new file mode 100644 index 0000000..1a1bede --- /dev/null +++ b/scripts/run_residue_controls.py @@ -0,0 +1,254 @@ +#!/usr/bin/env python3 +"""Generate cardinality- and residue-matched null ensembles for almost-prime supports. + +The primary run uses n=14, k=1,2,3, t=0,1,2,3 matched low-order bits, +and paired position/Fourier entropy calculations. +""" +from __future__ import annotations + +import argparse +import csv +import json +from pathlib import Path +import sys + +import numpy as np + +ROOT = Path(__file__).resolve().parents[1] +sys.path.insert(0, str(ROOT)) + +from subset_states.core import ( + entropy_from_state_vector, + entropy_from_support, + qft_state_from_support, +) +from subset_states.experiments import almost_prime_union_supports + + +def write_rows(path: Path, rows: list[dict]) -> None: + path.parent.mkdir(parents=True, exist_ok=True) + with path.open("w", newline="") as handle: + writer = csv.DictWriter(handle, fieldnames=list(rows[0].keys())) + writer.writeheader() + writer.writerows(rows) + + +def shannon_bits(counts: np.ndarray) -> float: + counts = np.asarray(counts, dtype=np.float64) + total = counts.sum() + if total <= 0: + return 0.0 + p = counts[counts > 0] / total + return float(-np.sum(p * np.log2(p))) + + +def residue_counts(support: np.ndarray, modulus: int) -> np.ndarray: + return np.bincount(support % modulus, minlength=modulus).astype(np.int64) + + +def sample_matched_support( + n: int, + counts: np.ndarray, + modulus: int, + rng: np.random.Generator, +) -> np.ndarray: + N = 1 << n + parts: list[np.ndarray] = [] + for residue, count in enumerate(counts): + count = int(count) + if count == 0: + continue + pool = np.arange(residue, N, modulus, dtype=np.int64) + if count > pool.size: + raise ValueError( + f"cannot draw {count} labels from residue {residue} mod {modulus}; " + f"pool has size {pool.size}" + ) + parts.append(rng.choice(pool, size=count, replace=False).astype(np.int64)) + if not parts: + raise ValueError("matched support would be empty") + return np.sort(np.concatenate(parts)) + + +def summarize(values: np.ndarray) -> dict[str, float | int]: + values = np.asarray(values, dtype=np.float64) + std = float(values.std(ddof=1)) if values.size > 1 else 0.0 + q025, q25, q50, q75, q975 = np.quantile(values, [0.025, 0.25, 0.5, 0.75, 0.975]) + return { + "count": int(values.size), + "mean": float(values.mean()), + "std": std, + "sem": float(std / np.sqrt(values.size)) if values.size > 1 else 0.0, + "q025": float(q025), + "q25": float(q25), + "median": float(q50), + "q75": float(q75), + "q975": float(q975), + "minimum": float(values.min()), + "maximum": float(values.max()), + } + + +def main() -> None: + parser = argparse.ArgumentParser() + parser.add_argument("--n", type=int, default=14) + parser.add_argument("--k-values", type=int, nargs="+", default=[1, 2, 3]) + parser.add_argument("--matched-bits", type=int, nargs="+", default=[0, 1, 2, 3]) + parser.add_argument("--samples", type=int, default=1000) + parser.add_argument("--seed", type=int, default=2026081701) + parser.add_argument("--outdir", type=Path, default=ROOT / "data") + args = parser.parse_args() + + if args.n <= 0 or args.n % 2: + raise ValueError("n must be a positive even integer") + if any(t < 0 or t > args.n // 2 for t in args.matched_bits): + raise ValueError("matched-bits must lie between 0 and n/2") + if args.samples < 2: + raise ValueError("samples must be at least 2") + + supports = dict(almost_prime_union_supports(args.n)) + summary_rows: list[dict] = [] + raw_rows: list[dict] = [] + bound_rows: list[dict] = [] + half = args.n // 2 + + structured: dict[int, tuple[float, float]] = {} + for k in args.k_values: + support = supports[k] + structured[k] = ( + entropy_from_support(args.n, support), + entropy_from_state_vector(args.n, qft_state_from_support(args.n, support)), + ) + + for k in args.k_values: + support = supports[k] + M = int(support.size) + structured_position, structured_fourier = structured[k] + for t in args.matched_bits: + modulus = 1 << t + counts = residue_counts(support, modulus) + H_res = shannon_bits(counts) + ceiling = float(half - t + H_res) + forced_gap = float(half - ceiling) + seed = int(args.seed + 1000 * k + 37 * t) + rng = np.random.default_rng(seed) + position = np.empty(args.samples, dtype=np.float64) + fourier = np.empty(args.samples, dtype=np.float64) + + for sample in range(args.samples): + matched = sample_matched_support(args.n, counts, modulus, rng) + position[sample] = entropy_from_support(args.n, matched) + fourier[sample] = entropy_from_state_vector( + args.n, qft_state_from_support(args.n, matched) + ) + raw_rows.append( + { + "n": args.n, + "k": k, + "M": M, + "matched_low_bits": t, + "modulus": modulus, + "sample": sample, + "seed": seed, + "position_entropy": float(position[sample]), + "fourier_entropy": float(fourier[sample]), + "fourier_minus_position": float(fourier[sample] - position[sample]), + } + ) + + ps = summarize(position) + fs = summarize(fourier) + position_residual = float(ps["mean"] - structured_position) + fourier_residual = float(fs["mean"] - structured_fourier) + summary_rows.append( + { + "n": args.n, + "k": k, + "M": M, + "matched_low_bits": t, + "modulus": modulus, + "samples": args.samples, + "seed": seed, + "residue_counts": json.dumps(counts.tolist(), separators=(",", ":")), + "residue_entropy_bits": H_res, + "entropy_ceiling_bits": ceiling, + "forced_gap_from_balanced_max_bits": forced_gap, + "structured_position_entropy": structured_position, + "structured_fourier_entropy": structured_fourier, + "null_position_mean": ps["mean"], + "null_position_std": ps["std"], + "null_position_sem": ps["sem"], + "null_position_q025": ps["q025"], + "null_position_median": ps["median"], + "null_position_q975": ps["q975"], + "null_position_min": ps["minimum"], + "null_position_max": ps["maximum"], + "position_residual_deficit": position_residual, + "position_standardized_deficit": float(position_residual / ps["std"]) if ps["std"] else float("inf"), + "position_null_count_at_or_below_structured": int(np.count_nonzero(position <= structured_position)), + "null_fourier_mean": fs["mean"], + "null_fourier_std": fs["std"], + "null_fourier_sem": fs["sem"], + "null_fourier_q025": fs["q025"], + "null_fourier_median": fs["median"], + "null_fourier_q975": fs["q975"], + "null_fourier_min": fs["minimum"], + "null_fourier_max": fs["maximum"], + "fourier_residual_deficit": fourier_residual, + "fourier_standardized_deficit": float(fourier_residual / fs["std"]) if fs["std"] else float("inf"), + "fourier_null_count_at_or_below_structured": int(np.count_nonzero(fourier <= structured_fourier)), + "paired_null_fourier_minus_position_mean": float(np.mean(fourier - position)), + "paired_null_fourier_minus_position_std": float(np.std(fourier - position, ddof=1)), + } + ) + bound_rows.append( + { + "n": args.n, + "k": k, + "M": M, + "matched_low_bits": t, + "modulus": modulus, + "residue_counts": json.dumps(counts.tolist(), separators=(",", ":")), + "residue_probabilities": json.dumps((counts / M).tolist(), separators=(",", ":")), + "residue_entropy_bits": H_res, + "entropy_ceiling_bits": ceiling, + "forced_gap_from_balanced_max_bits": forced_gap, + "structured_position_entropy": structured_position, + "ceiling_minus_structured_entropy": float(ceiling - structured_position), + } + ) + print( + f"k={k}, t={t}, M={M}: " + f"position residual={position_residual:.6f}, " + f"Fourier residual={fourier_residual:.6f}" + ) + + # Deficit reductions relative to the cardinality-matched reference. + for k in args.k_values: + base = next( + row for row in summary_rows if row["k"] == k and row["matched_low_bits"] == 0 + ) + pos0 = float(base["position_residual_deficit"]) + four0 = float(base["fourier_residual_deficit"]) + for row in summary_rows: + if row["k"] != k: + continue + row["cardinality_deficit_reduction_position"] = ( + float(1.0 - float(row["position_residual_deficit"]) / pos0) + if pos0 != 0 + else float("nan") + ) + row["cardinality_deficit_reduction_fourier"] = ( + float(1.0 - float(row["fourier_residual_deficit"]) / four0) + if four0 != 0 + else float("nan") + ) + + args.outdir.mkdir(parents=True, exist_ok=True) + write_rows(args.outdir / "residue_matched_summary.csv", summary_rows) + write_rows(args.outdir / "residue_matched_samples.csv", raw_rows) + write_rows(args.outdir / "residue_entropy_bounds.csv", bound_rows) + + +if __name__ == "__main__": + main() diff --git a/scripts/run_smoke_tests.py b/scripts/run_smoke_tests.py index a66b880..1c35cab 100644 --- a/scripts/run_smoke_tests.py +++ b/scripts/run_smoke_tests.py @@ -1,69 +1,20 @@ #!/usr/bin/env python3 -"""Small deterministic checks for the subset-state utilities.""" +"""Run the lightweight scientific regression tests without pytest.""" from __future__ import annotations from pathlib import Path import sys +import unittest ROOT = Path(__file__).resolve().parents[1] sys.path.insert(0, str(ROOT)) -import numpy as np - -from subset_states.peak_fitting import local_m_grid, quadratic_peak_fit -from subset_states.tables import PEAK_M, read_table_i - -from subset_states.core import ( - balanced_bipartitions, - dnm_approximation, - entropy_from_state_vector, - entropy_from_support, - exact_page_entropy_bits, - omega_prime_factors_sieve, - qft_state_from_support, - random_subset, - tnm_approximation, -) - def main() -> None: - rng = np.random.default_rng(123) - n = 4 - N = 1 << n - - # M=1 and M=N are product states for the natural bipartition. - assert abs(entropy_from_support(n, np.array([3]))) < 1e-12 - assert abs(entropy_from_support(n, np.arange(N))) < 1e-12 - - # A two-Bell-pair/rainbow support has entropy n/2 for n=4. - rainbow = np.array([0b0011, 0b0110, 0b1001, 0b1100]) - assert abs(entropy_from_support(n, rainbow) - 2.0) < 1e-12 - - support = random_subset(n, 5, rng) - qft_state = qft_state_from_support(n, support) - assert abs(np.linalg.norm(qft_state) - 1.0) < 1e-12 - _ = entropy_from_state_vector(n, qft_state) - - partitions = list(balanced_bipartitions(10)) - assert len(partitions) == 126 - - omega = omega_prime_factors_sieve(16) - assert omega[0] == 0 and omega[1] == 0 and omega[8] == 3 and omega[12] == 3 - - assert abs(dnm_approximation(n, 1)) < 1e-12 - assert tnm_approximation(n, 0) > 0 - assert abs(tnm_approximation(n, N)) < 1e-12 - assert exact_page_entropy_bits(10) > 0 - - table = read_table_i(ROOT / "data" / "table_i_peaks.csv") - assert table[0]["n"] == 10 and PEAK_M[14] == 716 - - grid = local_m_grid(10, PEAK_M[10], points=5, span=0.1) - assert PEAK_M[10] in grid and grid.size >= 5 - fit = quadratic_peak_fit(np.array([80, 107, 140]), np.array([4.0, 4.1, 4.0]), np.array([0.01, 0.01, 0.01])) - assert "fit_status" in fit and fit["M_peak"] > 0 - - print("smoke tests passed") + suite = unittest.defaultTestLoader.discover(str(ROOT / "tests"), pattern="test_*.py") + result = unittest.TextTestRunner(verbosity=2).run(suite) + if not result.wasSuccessful(): + raise SystemExit(1) if __name__ == "__main__": diff --git a/scripts/validate_residue_results.py b/scripts/validate_residue_results.py new file mode 100644 index 0000000..81ffaae --- /dev/null +++ b/scripts/validate_residue_results.py @@ -0,0 +1,76 @@ +#!/usr/bin/env python3 +from __future__ import annotations +import csv, json, math, sys +from itertools import combinations +from pathlib import Path +import numpy as np +ROOT=Path(__file__).resolve().parents[1];sys.path.insert(0,str(ROOT)) +from subset_states.core import entropy_from_support, matrix_from_support +from subset_states.experiments import almost_prime_union_supports + +def H(counts): + c=np.asarray(counts,dtype=float);p=c[c>0]/c.sum();return float(-np.sum(p*np.log2(p))) if p.size else 0.0 + +def direct_entropy(n,support): + omega=matrix_from_support(n,support);rho=omega.conj().T@omega + w=np.linalg.eigvalsh(rho).real;w=w[w>1e-14];w=w/w.sum();return float(-np.sum(w*np.log2(w))) + +def main(): + out=[];n=4;N=1<>i&1),dtype=np.int64) + S=entropy_from_support(n,s);max_direct=max(max_direct,abs(S-direct_entropy(n,s))) + for t in (1,2): + q=1<1e-10 or max_direct>1e-10 or single_class_violation>1e-10 or max_mean_err>1e-12 or max_std_err>1e-12 or not all_counts or not all_below: raise SystemExit(1) +if __name__=='__main__':main() diff --git a/subset_states/__init__.py b/subset_states/__init__.py index 8a97382..b95a981 100644 --- a/subset_states/__init__.py +++ b/subset_states/__init__.py @@ -2,21 +2,27 @@ from .peak_fitting import local_m_grid, quadratic_peak_fit from .tables import PEAK_M, PEAK_S, TABLE_I_PEAKS, read_table_i, table_i_array - from .core import ( + average_entropy_lower_bound_from_purity, balanced_bipartitions, + dense_bulk_approximation, dnm_approximation, entropy_from_state_vector, + fixed_cardinality_average_purity, entropy_from_support, exact_page_entropy_bits, + fixed_cardinality_mean_spectrum, + hypergeometric_occupancy_approximation, matrix_from_state_vector, matrix_from_support, + mean_matrix_uniform_eigenvalue, natural_right_bits, omega_prime_factors_sieve, qft_state_from_support, random_balanced_partition, random_subset, renyi_entropy_from_spectrum, + residue_class_entropy_ceiling, spectrum_from_matrix, summary_stats, tnm_approximation, @@ -30,19 +36,26 @@ "quadratic_peak_fit", "read_table_i", "table_i_array", + "average_entropy_lower_bound_from_purity", "balanced_bipartitions", + "dense_bulk_approximation", "dnm_approximation", "entropy_from_state_vector", + "fixed_cardinality_average_purity", "entropy_from_support", "exact_page_entropy_bits", + "fixed_cardinality_mean_spectrum", + "hypergeometric_occupancy_approximation", "matrix_from_state_vector", "matrix_from_support", + "mean_matrix_uniform_eigenvalue", "natural_right_bits", "omega_prime_factors_sieve", "qft_state_from_support", "random_balanced_partition", "random_subset", "renyi_entropy_from_spectrum", + "residue_class_entropy_ceiling", "spectrum_from_matrix", "summary_stats", "tnm_approximation", diff --git a/subset_states/core.py b/subset_states/core.py index 7c24dc2..d503aab 100644 --- a/subset_states/core.py +++ b/subset_states/core.py @@ -7,7 +7,7 @@ import numpy as np from numpy.typing import ArrayLike, NDArray -from scipy.special import gammaln, logsumexp, xlogy, digamma +from scipy.special import digamma, gammaln, logsumexp, xlogy @dataclass(frozen=True) @@ -27,6 +27,13 @@ def _validate_even_n(n: int) -> None: raise ValueError(f"n must be a positive even integer; received n={n}.") +def _validate_support_size(n: int, m: int, *, allow_zero: bool = False) -> None: + N = 1 << n + lower = 0 if allow_zero else 1 + if not (lower <= m <= N): + raise ValueError(f"m must satisfy {lower} <= m <= 2**n={N}; received m={m}.") + + def natural_right_bits(n: int) -> tuple[int, ...]: """Return the natural right subsystem: the low-order n/2 bits.""" @@ -48,18 +55,12 @@ def random_subset(n: int, m: int, rng: np.random.Generator) -> NDArray[np.int64] if n <= 0: raise ValueError("n must be positive.") - N = 1 << n - if not (1 <= m <= N): - raise ValueError(f"m must satisfy 1 <= m <= 2**n={N}; received m={m}.") - return np.sort(rng.choice(N, size=m, replace=False).astype(np.int64)) + _validate_support_size(n, m) + return np.sort(rng.choice(1 << n, size=m, replace=False).astype(np.int64)) def project_bits(values: ArrayLike, bit_positions: Sequence[int]) -> NDArray[np.int64]: - """Project integer labels onto selected bit positions. - - Bit positions are counted from the least-significant bit. The first entry of - ``bit_positions`` becomes the least-significant bit of the projected label. - """ + """Project integer labels onto selected bit positions.""" values_u = np.asarray(values, dtype=np.uint64) out = np.zeros(values_u.shape, dtype=np.uint64) @@ -76,10 +77,11 @@ def matrix_from_support( normalize: bool = True, dtype: np.dtype | type = np.float64, ) -> NDArray: - """Return the bipartite coefficient matrix Ω for an equal-amplitude support. + """Return the bipartite coefficient matrix for an equal-amplitude support. - The reduced density matrix of the right subsystem is Ω†Ω. For a subset state - with M occupied basis states, the non-zero entries of Ω are 1/sqrt(M). + With ``normalize=True``, each occupied entry equals 1/sqrt(M), so the reduced + density matrix of the right subsystem is ``C.conj().T @ C``. Set + ``normalize=False`` to obtain the binary support-incidence matrix. """ _validate_even_n(n) @@ -99,14 +101,12 @@ def matrix_from_support( raise ValueError(f"balanced bipartition requires {n // 2} right bits.") left = _left_bits(n, right) - dim_left = 1 << len(left) - dim_right = 1 << len(right) - omega = np.zeros((dim_left, dim_right), dtype=dtype) + matrix = np.zeros((1 << len(left), 1 << len(right)), dtype=dtype) rows = project_bits(support_arr, left) cols = project_bits(support_arr, right) amp = 1.0 / sqrt(support_arr.size) if normalize else 1.0 - omega[rows, cols] = amp - return omega + matrix[rows, cols] = amp + return matrix def matrix_from_state_vector( @@ -114,7 +114,7 @@ def matrix_from_state_vector( state: ArrayLike, right_bits: Sequence[int] | None = None, ) -> NDArray: - """Return the bipartite coefficient matrix Ω for an arbitrary state vector.""" + """Return the bipartite coefficient matrix for an arbitrary state vector.""" _validate_even_n(n) vector = np.asarray(state) @@ -126,17 +126,16 @@ def matrix_from_state_vector( raise ValueError(f"balanced bipartition requires {n // 2} right bits.") left = _left_bits(n, right) - # NumPy's reshape axes correspond to |x_{n-1}> ⊗ ... ⊗ |x_0>. left_axes = [n - 1 - bit for bit in left] right_axes = [n - 1 - bit for bit in right] tensor = vector.reshape((2,) * n) return np.transpose(tensor, left_axes + right_axes).reshape(1 << len(left), 1 << len(right)) -def spectrum_from_matrix(omega: ArrayLike, *, atol: float = 1e-14) -> NDArray[np.float64]: - """Return the non-zero eigenvalues of Ω†Ω using a stable SVD.""" +def spectrum_from_matrix(matrix: ArrayLike, *, atol: float = 1e-14) -> NDArray[np.float64]: + """Return the non-zero eigenvalues of C†C using a stable SVD.""" - mat = np.asarray(omega) + mat = np.asarray(matrix) singular_values = np.linalg.svd(mat, compute_uv=False) eigvals = np.real_if_close(singular_values * singular_values).astype(np.float64) eigvals[eigvals < atol] = 0.0 @@ -144,9 +143,7 @@ def spectrum_from_matrix(omega: ArrayLike, *, atol: float = 1e-14) -> NDArray[np total = eigvals.sum() if total <= 0: raise ValueError("density-matrix spectrum has zero trace.") - # Renormalize tiny numerical trace drift, but leave exact spectra unchanged. - eigvals = eigvals / total - return np.sort(eigvals) + return np.sort(eigvals / total) def renyi_entropy_from_spectrum( @@ -176,8 +173,8 @@ def entropy_from_support( *, order: float = 1.0, ) -> float: - omega = matrix_from_support(n, support, right_bits) - return renyi_entropy_from_spectrum(spectrum_from_matrix(omega), order=order) + matrix = matrix_from_support(n, support, right_bits) + return renyi_entropy_from_spectrum(spectrum_from_matrix(matrix), order=order) def entropy_from_state_vector( @@ -187,26 +184,28 @@ def entropy_from_state_vector( *, order: float = 1.0, ) -> float: - omega = matrix_from_state_vector(n, state, right_bits) - return renyi_entropy_from_spectrum(spectrum_from_matrix(omega), order=order) + matrix = matrix_from_state_vector(n, state, right_bits) + return renyi_entropy_from_spectrum(spectrum_from_matrix(matrix), order=order) def qft_state_from_support(n: int, support: ArrayLike) -> NDArray[np.complex128]: - """Return the normalized QFT of an equal-amplitude subset state.""" + """Return the positive-exponent QFT of an equal-amplitude subset state. + + NumPy's ``ifft(..., norm='ortho')`` implements the convention + exp(+2πijk/N)/sqrt(N), matching the manuscript definition. For the real + input states used here, switching the sign only complex-conjugates the output + and therefore leaves all reported entropies unchanged. + """ N = 1 << n support_arr = np.asarray(support, dtype=np.int64) vector = np.zeros(N, dtype=np.complex128) vector[support_arr] = 1.0 / sqrt(support_arr.size) - return np.fft.fft(vector, norm="ortho") + return np.fft.ifft(vector, norm="ortho") def random_balanced_partition(n: int, rng: np.random.Generator) -> tuple[int, ...]: - """Sample a unique balanced bipartition, represented by right-subsystem bits. - - The complement of a bipartition gives the same entropy. To avoid double - counting, bit 0 is always assigned to the right subsystem. - """ + """Sample a unique balanced bipartition, represented by right-subsystem bits.""" _validate_even_n(n) other = rng.choice(np.arange(1, n), size=n // 2 - 1, replace=False) @@ -214,11 +213,7 @@ def random_balanced_partition(n: int, rng: np.random.Generator) -> tuple[int, .. def balanced_bipartitions(n: int) -> Iterable[tuple[int, ...]]: - """Yield every unique balanced bipartition once. - - The count is binomial(n, n/2)/2. Bit 0 is fixed in the right subsystem to - identify complementary bipartitions. - """ + """Yield every balanced bipartition once, identifying complements.""" _validate_even_n(n) for combo in combinations(range(1, n), n // 2 - 1): @@ -240,44 +235,154 @@ def summary_stats(values: ArrayLike) -> SummaryStats: ) -def tnm_approximation(n: int, m: int) -> float: - """Analytical approximation T_{N,M} from Eq. (25) of the draft.""" +def fixed_cardinality_mean_spectrum(n: int, m: int) -> tuple[float, float]: + """Eigenvalues of E[rho] for the exact fixed-cardinality ensemble. + + For a balanced cut with d=2^(n/2) and N=d^2, the diagonal entries of E[rho] + equal 1/d and the off-diagonal entries equal (M-1)/(d(N-1)). The returned + pair is ``(uniform_mode, orthogonal_mode)``; the second eigenvalue has + multiplicity d-1. + """ + _validate_even_n(n) + _validate_support_size(n, m) + d = 1 << (n // 2) N = 1 << n - if m < 0 or m > N: - raise ValueError(f"m must satisfy 0 <= m <= {N}.") - c = log2(np.e) / 2.0 + off_diagonal = (m - 1) / (d * (N - 1)) + uniform_mode = 1.0 / d + (d - 1) * off_diagonal + orthogonal_mode = 1.0 / d - off_diagonal + return float(uniform_mode), float(orthogonal_mode) + + +def mean_matrix_uniform_eigenvalue(n: int, m: int) -> float: + """Uniform-mode eigenvalue of the exact mean reduced density matrix.""" + + return fixed_cardinality_mean_spectrum(n, m)[0] + + +def dense_bulk_approximation(n: int, m: int) -> float: + """Dense-bulk entropy ansatz using the exact mean-matrix uniform mode. + + The first moment is exact for the fixed-cardinality ensemble; treating its + uniform-mode eigenvalue as the separated eigenvalue of a typical sample is + still a mean-field approximation. + """ + + _validate_even_n(n) + _validate_support_size(n, m, allow_zero=True) if m == 0: - return n / 2.0 - c - if m == N: + # Retain the old formal Page-limit value for backward compatibility. + return n / 2.0 - log2(np.e) / 2.0 + if m == (1 << n): return 0.0 - return float(((N - m) * (1.5 * n - log2(N - m) - c) + m * (n - log2(m))) / N) + d = 1 << (n // 2) + lam = mean_matrix_uniform_eigenvalue(n, m) + remainder = 1.0 - lam + entropy_nats = ( + remainder * (np.log(d) - np.log(remainder) - 0.5) + - lam * np.log(lam) + ) + return float(entropy_nats / np.log(2.0)) -def dnm_approximation(n: int, m: int) -> float: - """Sparse balls-in-boxes approximation D_{N,M} from Appendix C. - This evaluates the binomial expression directly in log space, avoiding the - Monte Carlo noise present in the original script. +def hypergeometric_occupancy_approximation(n: int, m: int) -> float: + """Exact fixed-cardinality diagonal-occupancy entropy in bits. + + A column contains d of the N=d^2 support locations. Its occupancy W is + Hypergeometric(N, d, M), not Binomial(M, 1/d). The returned quantity is the + expected Shannon entropy of the diagonal of rho. It is an upper bound on + the von Neumann entropy and a sparse-regime approximation when off-diagonal + coherences are negligible. """ _validate_even_n(n) if m <= 0: return 0.0 - boxes = 1 << (n // 2) - if m == 1: - return 0.0 - w = np.arange(1, m + 1, dtype=np.float64) - log_q = ( - gammaln(m + 1) - - gammaln(w + 1) - - gammaln(m - w + 1) - + w * np.log(1.0 / boxes) - + (m - w) * np.log1p(-1.0 / boxes) + _validate_support_size(n, m) + d = 1 << (n // 2) + N = 1 << n + w_min = max(0, m - (N - d)) + w_max = min(d, m) + w = np.arange(w_min, w_max + 1, dtype=np.float64) + + def log_choose(total: int, chosen: np.ndarray | float) -> np.ndarray: + return gammaln(total + 1.0) - gammaln(chosen + 1.0) - gammaln(total - chosen + 1.0) + + log_prob = ( + log_choose(d, w) + + log_choose(N - d, m - w) + - (gammaln(N + 1.0) - gammaln(m + 1.0) - gammaln(N - m + 1.0)) ) - weights = np.exp(log_q) - p = w / m - return float(-boxes * np.sum(weights * p * np.log2(p))) + log_prob -= logsumexp(log_prob) + prob = np.exp(log_prob) + positive = w > 0 + p_diag = w[positive] / m + return float(-d * np.sum(prob[positive] * xlogy(p_diag, p_diag)) / np.log(2.0)) + + + +def fixed_cardinality_average_purity(n: int, m: int) -> float: + """Exact ensemble-average purity for the balanced fixed-cardinality ensemble. + + For N=2**n=d**2 and a support chosen uniformly among all M-element subsets, + this returns E[Tr(rho_R**2)] as derived in the manuscript. + """ + + _validate_even_n(n) + _validate_support_size(n, m) + d = 1 << (n // 2) + N = 1 << n + return float( + 1.0 / m + + 2.0 * (d - 1) * (m - 1) / (m * (N - 1)) + + (d - 1) ** 2 * (m - 1) * (m - 2) * (m - 3) + / (m * (N - 1) * (N - 2) * (N - 3)) + ) + + +def average_entropy_lower_bound_from_purity(n: int, m: int) -> float: + """Rigorous lower bound -log2(E[Tr(rho_R**2)]) on average entropy.""" + + return float(-np.log2(fixed_cardinality_average_purity(n, m))) + + +def residue_class_entropy_ceiling(n: int, support: ArrayLike, matched_low_bits: int) -> float: + """Entropy ceiling from populations modulo 2**matched_low_bits. + + For the natural balanced cut, if p_r is the support population in residue + class r modulo 2**t, then S <= n/2 - t + H_2(p). The case t=1 is the + parity ceiling. + """ + + _validate_even_n(n) + t = int(matched_low_bits) + if not (0 <= t <= n // 2): + raise ValueError(f"matched_low_bits must lie in [0, {n // 2}].") + support_arr = np.asarray(support, dtype=np.int64) + if support_arr.ndim != 1 or support_arr.size == 0: + raise ValueError("support must be a nonempty one-dimensional array.") + N = 1 << n + if np.any(support_arr < 0) or np.any(support_arr >= N): + raise ValueError(f"support labels must lie in [0, {N - 1}].") + if np.unique(support_arr).size != support_arr.size: + raise ValueError("support contains duplicate basis labels.") + modulus = 1 << t + counts = np.bincount(support_arr % modulus, minlength=modulus).astype(float) + probabilities = counts[counts > 0] / support_arr.size + shannon = float(-np.sum(probabilities * np.log2(probabilities))) if probabilities.size else 0.0 + return float(n / 2 - t + shannon) + +def tnm_approximation(n: int, m: int) -> float: + """Backward-compatible alias for :func:`dense_bulk_approximation`.""" + + return dense_bulk_approximation(n, m) + + +def dnm_approximation(n: int, m: int) -> float: + """Backward-compatible alias for the exact hypergeometric occupancy curve.""" + + return hypergeometric_occupancy_approximation(n, m) def exact_page_entropy_bits(n: int) -> float: @@ -285,7 +390,6 @@ def exact_page_entropy_bits(n: int) -> float: _validate_even_n(n) d = 1 << (n // 2) - # Page formula: H_{d^2} - H_d - (d-1)/(2d), converted to bits. return float((digamma(d * d + 1) - digamma(d + 1) - (d - 1) / (2 * d)) / np.log(2.0)) @@ -306,7 +410,6 @@ def omega_prime_factors_sieve(N: int) -> NDArray[np.uint16]: power = p while power < N: omega[power:N:power] += 1 - # Avoid integer overflow and unnecessary work. if power > (N - 1) // p: break power *= p diff --git a/subset_states/csv_plotting.py b/subset_states/csv_plotting.py index e667df5..c790b09 100644 --- a/subset_states/csv_plotting.py +++ b/subset_states/csv_plotting.py @@ -4,7 +4,7 @@ import math import re from pathlib import Path -from typing import Iterable, Sequence +from typing import Sequence import matplotlib matplotlib.use("Agg", force=True) @@ -12,9 +12,14 @@ import numpy as np from scipy import stats -from .core import exact_page_entropy_bits +from .core import ( + dense_bulk_approximation, + exact_page_entropy_bits, + hypergeometric_occupancy_approximation, + mean_matrix_uniform_eigenvalue, +) from .experiments import write_rows -from .plotting import apply_journal_style, make_inset_axis, save_figure +from .plotting import COOL_PALETTE, apply_journal_style, save_figure def _coerce(value: str): @@ -47,9 +52,7 @@ def _str_arr(rows: Sequence[dict], key: str) -> np.ndarray: def _infer_n_from_m(rows: Sequence[dict]) -> int: mmax = int(max(float(row["m"]) for row in rows)) n = int(round(math.log2(mmax))) - if (1 << n) == mmax: - return n - return int(math.ceil(math.log2(mmax))) + return n if (1 << n) == mmax else int(math.ceil(math.log2(mmax))) def _fit_line(x: np.ndarray, y: np.ndarray) -> dict: @@ -68,6 +71,8 @@ def _fit_line(x: np.ndarray, y: np.ndarray) -> dict: def plot_fig1(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None) -> None: + """Plot the two averaging procedures with explicit entropy units.""" + data_dir = Path(data_dir) summary = read_csv_rows(data_dir / "fig1_summary.csv") zoom = read_csv_rows(data_dir / "fig1_zoom_summary.csv") @@ -83,12 +88,28 @@ def draw(axis, rows, markersize: float = 2.5): e_states = _arr(rows, "states_sem") y_part = _arr(rows, "partitions_mean") e_part = _arr(rows, "partitions_sem") - axis.errorbar(m, y_part, yerr=e_part, fmt="o-", markersize=markersize, capsize=1.5, label="fixed state, random partitions") - axis.errorbar(m, y_states, yerr=e_states, fmt="s--", markersize=markersize, capsize=1.5, label="fixed partition, random states") + axis.errorbar( + m, + y_part, + yerr=e_part, + fmt="o-", + markersize=markersize, + capsize=1.5, + label="fixed support, random balanced cuts", + ) + axis.errorbar( + m, + y_states, + yerr=e_states, + fmt="s--", + markersize=markersize, + capsize=1.5, + label="fixed cut, random supports", + ) draw(ax, summary) ax.set_xlabel(r"support size $M$") - ax.set_ylabel(r"entropy $S_{N,M}$") + ax.set_ylabel("mean entropy (bits)") ax.set_xlim(0, 1 << n) ax.set_ylim(0, n / 2) ax.legend(loc="lower center", bbox_to_anchor=(0.5, -0.38), ncol=1, frameon=False) @@ -98,19 +119,25 @@ def draw(axis, rows, markersize: float = 2.5): inset.set_xlim(0, max(float(row["m"]) for row in zoom) * 1.02) inset.set_ylim(max(0, n / 2 - 3), n / 2) inset.set_xlabel(r"$M$", labelpad=1) - inset.set_ylabel(r"$S$", labelpad=1) + inset.set_ylabel("bits", labelpad=1) inset.legend().remove() save_figure(fig, out_pdf) def plot_fig2(data_dir: str | Path, out_pdf: str | Path, *, write_fit_summary: bool = True) -> None: + """Plot Table-I scaling, retaining all n=10,...,30 points.""" + data_dir = Path(data_dir) rows = read_csv_rows(data_dir / "fig2_table_with_page.csv") n = _arr(rows, "n") M_n = _arr(rows, "M_n") S_n = _arr(rows, "S_n") log2_M = _arr(rows, "log2_M_n") if "log2_M_n" in rows[0] else np.log2(M_n) - page = _arr(rows, "Page_exact_bits") if "Page_exact_bits" in rows[0] else np.array([exact_page_entropy_bits(int(x)) for x in n]) + page = ( + _arr(rows, "Page_exact_bits") + if "Page_exact_bits" in rows[0] + else np.array([exact_page_entropy_bits(int(x)) for x in n]) + ) fit_logM = _fit_line(n, log2_M) fit_S = _fit_line(n, S_n) @@ -121,50 +148,104 @@ def plot_fig2(data_dir: str | Path, out_pdf: str | Path, *, write_fit_summary: b apply_journal_style() fig, ax = plt.subplots(figsize=(4.7, 3.6)) x = np.linspace(n.min() - 1, n.max() + 1, 200) - ax.plot(n, log2_M, "o", label=r"$\log_2 M_n$") - ax.plot(x, fit_logM["slope"] * x + fit_logM["intercept"], "--", linewidth=1) - ax.plot(n, S_n, "s", label=r"$S_n$") - ax.plot(x, fit_S["slope"] * x + fit_S["intercept"], "--", linewidth=1) - ax.plot(n, page, ":", label="Page average") + + points_m = ax.plot(n, log2_M, "o", label=r"$\log_2\widehat M_n$")[0] + ax.plot( + x, + fit_logM["slope"] * x + fit_logM["intercept"], + "--", + linewidth=1, + color=points_m.get_color(), + ) + points_s = ax.plot(n, S_n, "s", label=r"$\widehat S_n$")[0] + ax.plot( + x, + fit_S["slope"] * x + fit_S["intercept"], + "--", + linewidth=1, + color=points_s.get_color(), + ) + ax.plot(n, page, ":", label="Page mean") ax.set_xlabel(r"number of qubits $n$") - ax.set_ylabel("bits") + ax.set_ylabel("value (bits)") ax.set_xlim(n.min() - 1, n.max() + 1) + ax.set_xticks([10, 15, 20, 25, 30]) ax.set_ylim(0, max(log2_M.max(), page.max()) + 1) ax.legend(frameon=False, loc="upper left") save_figure(fig, out_pdf) def plot_fig3(data_dir: str | Path, out_pdf: str | Path, *, bins: int = 500) -> None: + """Plot the spectral bulk and compare three isolated-mode estimates.""" + data_dir = Path(data_dir) rows = read_csv_rows(data_dir / "fig3_spectrum.csv") eigvals = _arr(rows, "lambda") eigvals.sort() - bulk = eigvals[:-1] - positive_bulk = bulk[bulk > 0] + lambda0 = float(eigvals[-1]) + positive_bulk = eigvals[:-1] + positive_bulk = positive_bulk[positive_bulk > 0] if positive_bulk.size == 0: raise ValueError("fig3_spectrum.csv contains no positive bulk eigenvalues.") + summary_path = data_dir / "fig3_spectrum_summary.csv" + if not summary_path.exists(): + raise FileNotFoundError( + "fig3_spectrum_summary.csv is required for the fixed-cardinality mean-mode comparison." + ) + summary = read_csv_rows(summary_path)[0] + n = int(float(summary["n"])) + m = int(float(summary["M"])) + lambda_mf = mean_matrix_uniform_eigenvalue(n, m) + lambda_leading = m / (1 << n) + apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.6)) - ax.hist(positive_bulk, bins=bins) - ax.set_xlabel(r"eigenvalue $\lambda$ excluding $\lambda_0$") + fig, ax = plt.subplots(figsize=(4.9, 3.6)) + ax.hist(positive_bulk, bins=bins, color=COOL_PALETTE[0]) + ax.set_xlabel(r"bulk eigenvalue $\lambda$") ax.set_ylabel("count") ax.set_xlim(0, positive_bulk.max() * 1.05) + ax.set_title(rf"$n={n}$, $M={m:,}$", loc="left", pad=3) + + inset = ax.inset_axes((0.52, 0.52, 0.45, 0.41)) + values = np.asarray([lambda0, lambda_mf, lambda_leading]) + y = np.asarray([2, 1, 0]) + labels = [r"observed $\lambda_0$", r"mode of $\mathbb{E}[\rho]$", r"leading $M/N$"] + for value, yi, color in zip(values, y, COOL_PALETTE[:3]): + inset.plot(value, yi, "o", color=color, markersize=4) + inset.axvline(value, color=color, linewidth=0.8, alpha=0.45) + pad = max(values.max() - values.min(), 1e-6) * 0.18 + inset.set_xlim(values.min() - pad, values.max() + pad) + inset.set_ylim(-0.55, 2.55) + inset.set_yticks(y, labels) + inset.set_xlabel("isolated eigenvalue", labelpad=1) + inset.tick_params(axis="y", labelsize=6.8) + inset.tick_params(axis="x", labelsize=6.8) save_figure(fig, out_pdf) -def _draw_fig4(axis, rows, label_data: bool) -> None: - m = _arr(rows, "m") +def _draw_fig4(axis, rows: Sequence[dict], n: int, label_data: bool) -> None: + m = _arr(rows, "m").astype(int) mean = _arr(rows, "entropy_mean") sem = _arr(rows, "entropy_sem") - D = _arr(rows, "D_NM") - T = _arr(rows, "T_NM") - axis.errorbar(m, mean, yerr=sem, fmt="o", markersize=2.2, capsize=1.2, label=r"numerical $S_{N,M}$" if label_data else None) - axis.plot(m, D, ":", label=r"$D_{N,M}$" if label_data else None) - axis.plot(m, T, "--", label=r"$T_{N,M}$" if label_data else None) + sparse = np.asarray([hypergeometric_occupancy_approximation(n, int(x)) for x in m]) + dense = np.asarray([dense_bulk_approximation(n, int(x)) for x in m]) + axis.errorbar( + m, + mean, + yerr=sem, + fmt="o", + markersize=2.2, + capsize=1.2, + label="numerical mean" if label_data else None, + ) + axis.plot(m, sparse, ":", label=r"diagonal occupancy $D_{N,M}$" if label_data else None) + axis.plot(m, dense, "--", label=r"dense bulk $T_{N,M}$" if label_data else None) def plot_fig4(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None) -> None: + """Plot numerical data with corrected fixed-cardinality approximations.""" + data_dir = Path(data_dir) rows = read_csv_rows(data_dir / "fig4_summary.csv") zoom = read_csv_rows(data_dir / "fig4_zoom_summary.csv") @@ -173,23 +254,29 @@ def plot_fig4(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None apply_journal_style() fig, ax = plt.subplots(figsize=(4.7, 3.8)) - _draw_fig4(ax, rows, True) + _draw_fig4(ax, rows, n, True) ax.set_xlabel(r"support size $M$") - ax.set_ylabel("entropy") + ax.set_ylabel("entropy (bits)") ax.set_xlim(0, 1 << n) ax.set_ylim(0, n / 2) ax.legend(frameon=False, loc="lower center", bbox_to_anchor=(0.5, -0.35), ncol=3) inset = ax.inset_axes((0.59, 0.59, 0.38, 0.38)) - _draw_fig4(inset, zoom, False) + _draw_fig4(inset, zoom, n, False) inset.set_xlim(0, max(float(row["m"]) for row in zoom) * 1.02) inset.set_ylim(max(0, n / 2 - 3), n / 2) inset.set_xlabel(r"$M$", labelpad=1) - inset.set_ylabel(r"$S$", labelpad=1) + inset.set_ylabel("bits", labelpad=1) save_figure(fig, out_pdf) def plot_fig5(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None) -> None: + """Compare deterministic arithmetic supports with the random null distribution. + + The shaded regions are one ensemble standard deviation. They represent the + spread of the random-support null distribution, not uncertainty in its mean. + """ + data_dir = Path(data_dir) random_rows = read_csv_rows(data_dir / "fig5_random_qft_summary.csv") union_rows = read_csv_rows(data_dir / "fig5_almost_prime_unions.csv") @@ -198,24 +285,46 @@ def plot_fig5(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None m = _arr(random_rows, "m") pos = _arr(random_rows, "position_mean") - pos_sem = _arr(random_rows, "position_sem") + pos_std = _arr(random_rows, "position_std") qft = _arr(random_rows, "qft_mean") - qft_sem = _arr(random_rows, "qft_sem") + qft_std = _arr(random_rows, "qft_std") union_m = _arr(union_rows, "m") union_pos = _arr(union_rows, "position_entropy") union_qft = _arr(union_rows, "qft_entropy") apply_journal_style() - fig, ax = plt.subplots(figsize=(4.7, 3.6)) - ax.errorbar(m, pos, yerr=pos_sem, fmt="o", markersize=2, capsize=1.2, label=r"random subset") - ax.errorbar(m, qft, yerr=qft_sem, fmt=".", markersize=2, capsize=1.2, label=r"random subset after QFT") + fig, ax = plt.subplots(figsize=(4.7, 3.7)) + line_pos = ax.plot(m, pos, "-", linewidth=1.2, label=r"random supports: mean $\pm$ 1 SD")[0] + ax.fill_between( + m, + np.maximum(0.0, pos - pos_std), + np.minimum(n / 2, pos + pos_std), + color=line_pos.get_color(), + alpha=0.16, + linewidth=0, + ) + line_qft = ax.plot( + m, + qft, + "--", + linewidth=1.2, + label=r"after QFT: mean $\pm$ 1 SD", + )[0] + ax.fill_between( + m, + np.maximum(0.0, qft - qft_std), + np.minimum(n / 2, qft + qft_std), + color=line_qft.get_color(), + alpha=0.14, + linewidth=0, + ) ax.plot(union_m, union_pos, "+", markersize=6, label=r"$U_{N,k}$") ax.plot(union_m, union_qft, "x", markersize=5, label=r"QFT $U_{N,k}$") ax.set_xlabel(r"support size $M$") - ax.set_ylabel("entropy") + ax.set_ylabel("entropy (bits)") ax.set_xlim(0, 1 << n) ax.set_ylim(0, n / 2) - ax.legend(frameon=False, loc="lower center", bbox_to_anchor=(0.5, -0.45), ncol=2) + ax.legend(frameon=False, loc="lower center", bbox_to_anchor=(0.5, -0.46), ncol=2) save_figure(fig, out_pdf) @@ -227,18 +336,33 @@ def _order_key(value) -> float: def _rows_for_order(rows: Sequence[dict], order: float) -> tuple[np.ndarray, np.ndarray, np.ndarray]: - filtered = [row for row in rows if (_order_key(row["order"]) == order or (np.isinf(order) and np.isinf(_order_key(row["order"]))))] + filtered = [ + row + for row in rows + if _order_key(row["order"]) == order + or (np.isinf(order) and np.isinf(_order_key(row["order"]))) + ] return _arr(filtered, "m"), _arr(filtered, "mean"), _arr(filtered, "sem") -def _draw_fig6(axis, rows: Sequence[dict], markers: bool = True) -> None: +def _draw_fig6(axis, rows: Sequence[dict]) -> list: orders = [1.0, 2.0, np.inf] labels = {1.0: r"$S^{(1)}$", 2.0: r"$S^{(2)}$", np.inf: r"$S^{(\infty)}$"} styles = {1.0: "o-", 2.0: "s--", np.inf: "^:"} + handles = [] for order in orders: m, mean, sem = _rows_for_order(rows, order) - fmt = styles[order] if markers else styles[order].replace("o", "").replace("s", "").replace("^", "") - axis.errorbar(m, mean, yerr=sem, fmt=fmt, markersize=2.2, capsize=1.2, label=labels[order]) + handle = axis.errorbar( + m, + mean, + yerr=sem, + fmt=styles[order], + markersize=2.2, + capsize=1.2, + label=labels[order], + ) + handles.append(handle) + return handles def plot_fig6(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None) -> None: @@ -250,64 +374,94 @@ def plot_fig6(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None zoom_stop = int(max(float(row["m"]) for row in zoom)) apply_journal_style() - fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(4.7, 6.0), sharey=False) - _draw_fig6(ax1, rows) + fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(4.7, 5.7), sharey=False) + handles = _draw_fig6(ax1, rows) ax1.set_xlabel(r"support size $M$") - ax1.set_ylabel("Rényi entropy") + ax1.set_ylabel("Rényi entropy (bits)") ax1.set_xlim(0, 1 << n) ax1.set_ylim(0, n / 2) - ax1.legend(frameon=False, ncol=3, loc="lower center", bbox_to_anchor=(0.5, -0.42)) + ax1.text(0.02, 0.94, "full range", transform=ax1.transAxes, va="top", fontsize=8) _draw_fig6(ax2, zoom) ax2.set_xlabel(r"support size $M$") - ax2.set_ylabel("Rényi entropy") + ax2.set_ylabel("Rényi entropy (bits)") ax2.set_xlim(0, zoom_stop) ax2.set_ylim(max(0, n / 2 - 3), n / 2) - ax2.legend(frameon=False, ncol=3, loc="lower center", bbox_to_anchor=(0.5, -0.42)) - fig.subplots_adjust(hspace=0.55) + ax2.text(0.02, 0.94, "peak region", transform=ax2.transAxes, va="top", fontsize=8) + + labels = [r"$S^{(1)}$", r"$S^{(2)}$", r"$S^{(\infty)}$"] + fig.legend(handles=handles, labels=labels, frameon=False, ncol=3, loc="lower center") + fig.subplots_adjust(hspace=0.45, bottom=0.12) save_figure(fig, out_pdf) def _families(rows: Sequence[dict]) -> list[str]: - seen = [] - for fam in _str_arr(rows, "state_family" if "state_family" in rows[0] else "family"): - if fam not in seen: + key = "state_family" if "state_family" in rows[0] else "family" + seen: list[str] = [] + for fam in _str_arr(rows, key): + if str(fam) not in seen: seen.append(str(fam)) return seen -def plot_fig7(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None, bins: int = 60) -> None: +def plot_fig7(data_dir: str | Path, out_pdf: str | Path, *, n: int | None = None, bins: int = 100) -> None: + """Plot both bipartition distributions on a common entropy scale.""" + data_dir = Path(data_dir) rows = read_csv_rows(data_dir / "fig7_partition_samples.csv") summary_path = data_dir / "fig7_partition_summary.csv" - page = None - if summary_path.exists(): - summary = read_csv_rows(summary_path) - if n is None and summary and summary[0].get("n", "") != "": - n = int(float(summary[0]["n"])) - if summary and "Page_exact_bits" in summary[0]: - page = float(summary[0]["Page_exact_bits"]) - if n is None: - n = 20 - if page is None: - page = exact_page_entropy_bits(n) + summary = read_csv_rows(summary_path) if summary_path.exists() else [] + if n is None and summary and summary[0].get("n", "") != "": + n = int(float(summary[0]["n"])) + n = 20 if n is None else n + page = ( + float(summary[0]["Page_exact_bits"]) + if summary and "Page_exact_bits" in summary[0] + else exact_page_entropy_bits(n) + ) + m_subset = None + for row in summary: + if str(row.get("state_family", "")) == "subset" and row.get("M", "") != "": + m_subset = int(float(row["M"])) + + key = "state_family" if "state_family" in rows[0] else "family" + preferred = [fam for fam in ("subset", "complex_haar") if fam in _families(rows)] + families = preferred or _families(rows) + arrays = { + family: np.asarray( + [float(row["entropy"]) for row in rows if str(row[key]) == family], + dtype=float, + ) + for family in families + } + global_min = min(values.min() for values in arrays.values()) + global_max = max(values.max() for values in arrays.values()) + padding = 0.04 * (global_max - global_min) + lo, hi = global_min - padding, global_max + padding + bin_edges = np.linspace(lo, hi, bins + 1) - families = _families(rows) apply_journal_style() - fig, axes = plt.subplots(len(families), 1, figsize=(4.7, 2.9 * len(families))) + fig, axes = plt.subplots(len(families), 1, figsize=(4.7, 2.65 * len(families)), sharex=True) if len(families) == 1: axes = [axes] - for ax, family in zip(axes, families): - values = np.asarray([float(row["entropy"]) for row in rows if str(row["state_family"]) == family], dtype=float) - ax.hist(values, bins=bins) + for index, (ax, family) in enumerate(zip(axes, families)): + values = arrays[family] + ax.hist(values, bins=bin_edges) ax.axvline(values.mean(), linestyle="--", linewidth=1, label="sample mean") - ax.axvline(page, linestyle=":", linewidth=1, label="Page average") - label = "complex Haar" if family == "complex_haar" else family.replace("_", " ") - ax.set_xlabel("entropy") + ax.axvline(page, linestyle=":", linewidth=1, label="Page mean") + if family == "complex_haar": + title = "complex Haar state" + elif family == "subset" and m_subset is not None: + title = rf"peak-support subset state, $M={m_subset}$" + else: + title = family.replace("_", " ") ax.set_ylabel("count") - ax.set_title(label) - ax.legend(frameon=False) - fig.subplots_adjust(hspace=0.55) + ax.set_title(title) + ax.set_xlim(lo, hi) + if index == 0: + ax.legend(frameon=False, loc="upper right") + axes[-1].set_xlabel("entropy (bits)") + fig.subplots_adjust(hspace=0.30) save_figure(fig, out_pdf) @@ -318,12 +472,25 @@ def _n_from_fig8_path(path: Path) -> int: return int(match.group(1)) -def plot_fig8(data_dir: str | Path, out_pdf: str | Path, *, n_values: Sequence[int] | None = None, bins: int = 120) -> None: +def plot_fig8( + data_dir: str | Path, + out_pdf: str | Path, + *, + n_values: Sequence[int] | None = None, + bins: int = 120, +) -> None: + """Repository-only best-of-random-candidate screening figure. + + Histograms are normalized because the two sample pools have different sizes. + This exploratory plot is intentionally not part of the revised manuscript. + """ + data_dir = Path(data_dir) - if n_values: - files = [data_dir / f"fig8_samples_n{int(n)}.csv" for n in n_values] - else: - files = sorted(data_dir.glob("fig8_samples_n*.csv"), key=_n_from_fig8_path) + files = ( + [data_dir / f"fig8_samples_n{int(n)}.csv" for n in n_values] + if n_values + else sorted(data_dir.glob("fig8_samples_n*.csv"), key=_n_from_fig8_path) + ) if not files: raise FileNotFoundError(f"no fig8_samples_n*.csv files found in {data_dir}") @@ -334,22 +501,28 @@ def plot_fig8(data_dir: str | Path, out_pdf: str | Path, *, n_values: Sequence[i for ax, path in zip(axes, files): rows = read_csv_rows(path) n = _n_from_fig8_path(path) - families = _families(rows) + key = "family" if "family" in rows[0] else "state_family" arrays = [] - for family in families: - key = "family" if "family" in rows[0] else "state_family" - values = np.asarray([float(row["entropy"]) for row in rows if str(row[key]) == family], dtype=float) + for family in _families(rows): + values = np.asarray( + [float(row["entropy"]) for row in rows if str(row[key]) == family], + dtype=float, + ) arrays.append((family, values)) lo = min(values.min() for _, values in arrays) hi = max(values.max() for _, values in arrays) bin_edges = np.linspace(lo, hi, bins) for family, values in arrays: - label = "random subsets, natural partition" if family.startswith("random") else "selected subset, all partitions" - ax.hist(values, bins=bin_edges, alpha=0.65, label=label) + label = ( + "random supports, natural cut" + if family.startswith("random") + else "selected random candidate, all balanced cuts" + ) + ax.hist(values, bins=bin_edges, density=True, alpha=0.55, label=label) ax.axvline(values.mean(), linestyle="--" if family.startswith("random") else ":", linewidth=1) M = int(float(rows[0].get("M", rows[0].get("m", 0)))) - ax.set_xlabel("entropy") - ax.set_ylabel("count") + ax.set_xlabel("entropy (bits)") + ax.set_ylabel("density") ax.set_title(rf"$n={n}$, $M={M}$") ax.legend(frameon=False) fig.subplots_adjust(hspace=0.55) @@ -367,7 +540,11 @@ def plot_peak_search(samples_csv: str | Path, fit_csv: str | Path, out_pdf: str sem = _arr(samples, "sem") x = np.log2(m.astype(float)) x_fit = np.linspace(x.min(), x.max(), 300) - y_fit = float(fit["quadratic_a"]) * x_fit**2 + float(fit["quadratic_b"]) * x_fit + float(fit["quadratic_c"]) + y_fit = ( + float(fit["quadratic_a"]) * x_fit**2 + + float(fit["quadratic_b"]) * x_fit + + float(fit["quadratic_c"]) + ) apply_journal_style() fig, ax = plt.subplots(figsize=(4.7, 3.6)) @@ -375,6 +552,6 @@ def plot_peak_search(samples_csv: str | Path, fit_csv: str | Path, out_pdf: str ax.plot(x_fit, y_fit, "--", label="quadratic fit") ax.axvline(float(fit["log2_M_peak"]), linestyle=":", linewidth=1, label="estimated peak") ax.set_xlabel(r"$\log_2 M$") - ax.set_ylabel(r"$S_{N,M}$") + ax.set_ylabel("entropy (bits)") ax.legend(frameon=False) save_figure(fig, out_pdf) diff --git a/subset_states/experiments.py b/subset_states/experiments.py index 79d48a2..cec3358 100644 --- a/subset_states/experiments.py +++ b/subset_states/experiments.py @@ -27,8 +27,7 @@ def m_grid(start: int, stop: int, points: int, *, include_stop: bool = True) -> if points <= 1: return np.array([start], dtype=np.int64) - endpoint = include_stop - grid = np.linspace(start, stop, points, endpoint=endpoint) + grid = np.linspace(start, stop, points, endpoint=include_stop) grid = np.unique(np.rint(grid).astype(np.int64)) return grid[(grid >= start) & (grid <= stop)] @@ -43,8 +42,6 @@ def write_rows(path: str | Path, rows: Iterable[dict], fieldnames: Sequence[str] def read_csv_columns(path: str | Path) -> dict[str, NDArray]: - import csv - with Path(path).open(newline="") as handle: reader = csv.DictReader(handle) data: dict[str, list] = {name: [] for name in reader.fieldnames or []} @@ -105,8 +102,7 @@ def random_subset_qft_samples( for idx in range(samples): support = random_subset(n, m, rng) position[idx] = entropy_from_support(n, support) - fourier_state = qft_state_from_support(n, support) - fourier[idx] = entropy_from_state_vector(n, fourier_state) + fourier[idx] = entropy_from_state_vector(n, qft_state_from_support(n, support)) return position, fourier @@ -121,8 +117,7 @@ def partition_entropy_samples_for_fixed_subset( support = random_subset(n, m, rng) values = np.empty(samples, dtype=np.float64) for idx in range(samples): - right_bits = random_balanced_partition(n, rng) - values[idx] = entropy_from_support(n, support, right_bits) + values[idx] = entropy_from_support(n, support, random_balanced_partition(n, rng)) return values @@ -136,8 +131,7 @@ def partition_entropy_samples_for_state( rng = np.random.default_rng(seed) values = np.empty(samples, dtype=np.float64) for idx in range(samples): - right_bits = random_balanced_partition(n, rng) - values[idx] = entropy_from_state_vector(n, state, right_bits) + values[idx] = entropy_from_state_vector(n, state, random_balanced_partition(n, rng)) return values @@ -149,18 +143,13 @@ def complex_haar_state(n: int, *, seed: int) -> NDArray[np.complex128]: def almost_prime_union_supports(n: int) -> list[tuple[int, NDArray[np.int64]]]: - """Return supports U_{N,k} for k=1,...,n-1. - - U_{N,k} contains integers below 2**n with 1 <= Ω(x) <= k. Thus U_{N,n-1} - excludes both 0 and 1, as required by the usual definition of k-almost primes. - """ + """Return U_{N,k} with 1 <= Ω(x) <= k, for k=1,...,n-1.""" N = 1 << n omega = omega_prime_factors_sieve(N) supports: list[tuple[int, NDArray[np.int64]]] = [] for k in range(1, n): - support = np.flatnonzero((omega >= 1) & (omega <= k)).astype(np.int64) - supports.append((k, support)) + supports.append((k, np.flatnonzero((omega >= 1) & (omega <= k)).astype(np.int64))) return supports diff --git a/subset_states/peak_fitting.py b/subset_states/peak_fitting.py index fcb7c58..77583c1 100644 --- a/subset_states/peak_fitting.py +++ b/subset_states/peak_fitting.py @@ -5,25 +5,14 @@ from numpy.typing import ArrayLike, NDArray -def local_m_grid(n: int, center: int, *, points: int, span: float | None = 0.25, half_width: int | None = None) -> NDArray[np.int64]: - """Return a sorted integer grid of support sizes around a tabulated peak. - - Parameters - ---------- - n: - Number of qubits. The allowed support sizes are 1 <= M <= 2**n. - center: - Tabulated peak support size M_n. - points: - Number of grid points requested. The center is always included. - span: - Fractional half-width of the grid, used when ``half_width`` is not given. - For example, span=0.20 gives approximately [0.8 center, 1.2 center]. - half_width: - Optional absolute half-width around center. If supplied, it overrides - ``span``. - """ - +def local_m_grid( + n: int, + center: int, + *, + points: int, + span: float | None = 0.25, + half_width: int | None = None, +) -> NDArray[np.int64]: if n <= 0: raise ValueError("n must be positive.") N = 1 << n @@ -31,21 +20,17 @@ def local_m_grid(n: int, center: int, *, points: int, span: float | None = 0.25, raise ValueError(f"center must satisfy 1 <= center <= 2**n={N}; got {center}.") if points < 3: raise ValueError("points must be at least 3 for a quadratic fit.") - if half_width is not None: width = int(half_width) if width <= 0: raise ValueError("half_width must be positive.") - low = max(1, center - width) - high = min(N, center + width) + low, high = max(1, center - width), min(N, center + width) else: - if span is None: - span = 0.25 + span = 0.25 if span is None else span if not (0 < span <= 1): raise ValueError("span must satisfy 0 < span <= 1.") low = max(1, int(round(center * (1.0 - span)))) high = min(N, int(round(center * (1.0 + span)))) - grid = np.unique(np.rint(np.linspace(low, high, points)).astype(np.int64)) grid = np.unique(np.concatenate([grid, np.asarray([center], dtype=np.int64)])) grid = grid[(grid >= 1) & (grid <= N)] @@ -54,81 +39,38 @@ def local_m_grid(n: int, center: int, *, points: int, span: float | None = 0.25, return grid -def quadratic_peak_fit(m: ArrayLike, mean: ArrayLike, sem: ArrayLike | None = None) -> dict[str, float | str | bool]: - """Fit mean entropy as a quadratic function of log2(M). - - The returned dictionary reports the quadratic coefficients, the estimated - peak, and a conservative status string. If the fitted parabola is not - concave or its maximum falls outside the sampled window, the best observed - grid point is reported instead of a fitted interior maximum. - """ - +def quadratic_peak_fit( + m: ArrayLike, + mean: ArrayLike, + sem: ArrayLike | None = None, +) -> dict[str, float | str | bool]: m_arr = np.asarray(m, dtype=np.float64) y = np.asarray(mean, dtype=np.float64) if m_arr.ndim != 1 or y.ndim != 1 or m_arr.size != y.size: raise ValueError("m and mean must be one-dimensional arrays of the same length.") - if m_arr.size < 3: - raise ValueError("at least 3 grid points are required for a quadratic fit.") - if np.any(m_arr <= 0): - raise ValueError("all support sizes M must be positive.") - + if m_arr.size < 3 or np.any(m_arr <= 0): + raise ValueError("at least three positive support sizes are required.") x = np.log2(m_arr) - weights = None if sem is not None: err = np.asarray(sem, dtype=np.float64) - if err.shape != y.shape: - raise ValueError("sem must have the same shape as mean.") positive = err[np.isfinite(err) & (err > 0)] if positive.size: - floor = positive.min() - weights = 1.0 / np.maximum(err, floor) - + weights = 1.0 / np.maximum(err, positive.min()) coeff = np.polyfit(x, y, deg=2, w=weights) a, b, c = [float(v) for v in coeff] - - cov = None - if x.size > 3: - try: - _, cov = np.polyfit(x, y, deg=2, w=weights, cov=True) - except Exception: - cov = None - best = int(np.argmax(y)) - status = "concave_quadratic" - interior_peak = False - + interior = False if a < 0: x_peak = -b / (2.0 * a) - interior_peak = bool(x.min() <= x_peak <= x.max()) - if interior_peak: - S_peak = c - b * b / (4.0 * a) - else: - status = "concave_quadratic_peak_outside_window_best_grid_point_reported" - x_peak = float(x[best]) - S_peak = float(y[best]) - else: - status = "non_concave_quadratic_best_grid_point_reported" + interior = bool(x.min() <= x_peak <= x.max()) + if a >= 0 or not interior: x_peak = float(x[best]) S_peak = float(y[best]) - - x_sem = float("nan") - S_sem = float("nan") - if cov is not None and a < 0 and interior_peak: - grad_x = np.asarray([b / (2.0 * a * a), -1.0 / (2.0 * a), 0.0]) - grad_S = np.asarray([b * b / (4.0 * a * a), -b / (2.0 * a), 1.0]) - x_var = float(grad_x @ cov @ grad_x) - S_var = float(grad_S @ cov @ grad_S) - x_sem = float(np.sqrt(max(x_var, 0.0))) - S_sem = float(np.sqrt(max(S_var, 0.0))) - elif sem is not None: - err = np.asarray(sem, dtype=np.float64) - if np.isfinite(err[best]): - S_sem = float(err[best]) - - M_peak = float(2.0**x_peak) - M_sem = float(np.log(2.0) * M_peak * x_sem) if np.isfinite(x_sem) else float("nan") - + status = "best_grid_point_reported" + else: + S_peak = c - b * b / (4.0 * a) + status = "concave_quadratic" return { "fit_status": status, "fit_variable": "log2_M", @@ -136,12 +78,12 @@ def quadratic_peak_fit(m: ArrayLike, mean: ArrayLike, sem: ArrayLike | None = No "quadratic_b": b, "quadratic_c": c, "log2_M_peak": float(x_peak), - "log2_M_peak_sem": x_sem, - "M_peak": M_peak, - "M_peak_sem": M_sem, + "log2_M_peak_sem": float("nan"), + "M_peak": float(2.0**x_peak), + "M_peak_sem": float("nan"), "S_peak": float(S_peak), - "S_peak_sem": S_sem, + "S_peak_sem": float("nan"), "best_grid_M": float(m_arr[best]), "best_grid_S": float(y[best]), - "peak_inside_window": bool(interior_peak), + "peak_inside_window": interior, } diff --git a/subset_states/plotting.py b/subset_states/plotting.py index 55c2f1b..55df510 100644 --- a/subset_states/plotting.py +++ b/subset_states/plotting.py @@ -7,8 +7,7 @@ import matplotlib.pyplot as plt from cycler import cycler -# A deliberately cool, non-warm palette: blue, teal, violet, slate, cyan, green-blue. -# Avoids orange/red/yellow so that all default plots have a cool visual tone. +# Cool, non-warm palette retained from the publication repository. COOL_PALETTE = [ "#25639C", # blue "#008C95", # teal @@ -22,24 +21,13 @@ def make_inset_axis(ax, bounds=(0.57, 0.55, 0.39, 0.39)): - """Create an inset axis without importing mpl_toolkits. - - Some Ubuntu/Python installations mix user-site Matplotlib with the system - mpl_toolkits package, which can break `mpl_toolkits.axes_grid1.inset_locator` - with an AttributeError involving matplotlib._docstring. Using the built-in - Axes.inset_axes method avoids that dependency entirely. The coordinates are - axis-relative: (left, bottom, width, height). - """ + """Create an inset axis using Matplotlib's built-in API.""" return ax.inset_axes(bounds) def apply_journal_style() -> None: - """Small, conservative figure defaults suitable for journal submission. - - The colour cycle is intentionally cool-toned; it avoids the default orange/red - entries that can dominate Matplotlib figures. - """ + """Conservative defaults suitable for the manuscript figures.""" plt.rcParams.update( { @@ -47,9 +35,11 @@ def apply_journal_style() -> None: "font.size": 9, "axes.labelsize": 9, "axes.titlesize": 9, + "axes.linewidth": 0.8, "legend.fontsize": 8, "xtick.labelsize": 8, "ytick.labelsize": 8, + "lines.linewidth": 1.15, "axes.prop_cycle": cycler(color=COOL_PALETTE), "pdf.fonttype": 42, "ps.fonttype": 42, @@ -62,6 +52,6 @@ def save_figure(fig, path: str | Path) -> None: path = Path(path) path.parent.mkdir(parents=True, exist_ok=True) fig.savefig(path) - # Store a PNG next to the PDF for quick inspection in repositories. if path.suffix.lower() == ".pdf": fig.savefig(path.with_suffix(".png"), dpi=300) + plt.close(fig) diff --git a/subset_states/tables.py b/subset_states/tables.py index 9d6f43a..5dddf41 100644 --- a/subset_states/tables.py +++ b/subset_states/tables.py @@ -8,9 +8,6 @@ import numpy as np from numpy.typing import NDArray -# Table I in the manuscript: peak-entanglement support size and peak entropy. -# These are treated as production values. The verification script samples locally -# around these M_n values; it is not intended to rediscover the peaks globally. TABLE_I_PEAKS: tuple[tuple[int, int, float], ...] = ( (10, 107, 4.072), (12, 276, 5.108), @@ -30,21 +27,12 @@ def table_i_array() -> NDArray[np.float64]: - """Return Table I as an array with columns n, M_n, S_n.""" - return np.asarray(TABLE_I_PEAKS, dtype=float) def read_table_i(path: str | Path | None = None) -> list[dict[str, int | float]]: - """Read a Table-I-style CSV file. - - The expected columns are ``n``, ``M_n`` and ``S_n``. Lines starting with ``#`` - are ignored so that the file can contain short comments. - """ - if path is None: return [{"n": n, "M_n": m, "S_n": s} for n, m, s in TABLE_I_PEAKS] - path = Path(path) with path.open(newline="") as handle: lines = [line for line in handle if line.strip() and not line.lstrip().startswith("#")] @@ -53,16 +41,16 @@ def read_table_i(path: str | Path | None = None) -> list[dict[str, int | float]] missing = required - set(reader.fieldnames or []) if missing: raise ValueError(f"{path} is missing required columns: {sorted(missing)}") + return [ + {"n": int(row["n"]), "M_n": int(row["M_n"]), "S_n": float(row["S_n"])} + for row in reader + ] - rows: list[dict[str, int | float]] = [] - for row in reader: - rows.append({"n": int(row["n"]), "M_n": int(row["M_n"]), "S_n": float(row["S_n"])}) - return rows - - -def select_table_rows(rows: Iterable[dict[str, int | float]], n_values: Iterable[int] | None = None) -> list[dict[str, int | float]]: - """Return table rows restricted to selected n values, preserving table order.""" +def select_table_rows( + rows: Iterable[dict[str, int | float]], + n_values: Iterable[int] | None = None, +) -> list[dict[str, int | float]]: selected = None if n_values is None else {int(n) for n in n_values} out = [row for row in rows if selected is None or int(row["n"]) in selected] if not out: diff --git a/tests/test_core.py b/tests/test_core.py new file mode 100644 index 0000000..53d1d8e --- /dev/null +++ b/tests/test_core.py @@ -0,0 +1,96 @@ +from __future__ import annotations + +from itertools import combinations +import unittest + +import numpy as np + +from subset_states.core import ( + dense_bulk_approximation, + entropy_from_state_vector, + fixed_cardinality_mean_spectrum, + hypergeometric_occupancy_approximation, + matrix_from_support, + qft_state_from_support, +) + + +class FixedCardinalityMeanTests(unittest.TestCase): + def test_spectrum_trace_and_endpoints(self) -> None: + for n in (4, 6, 8): + d = 1 << (n // 2) + N = 1 << n + for m in (1, max(2, N // 7), N): + uniform, orthogonal = fixed_cardinality_mean_spectrum(n, m) + self.assertAlmostEqual(uniform + (d - 1) * orthogonal, 1.0, places=13) + self.assertGreaterEqual(uniform, orthogonal) + self.assertGreaterEqual(orthogonal, -1e-14) + uniform, orthogonal = fixed_cardinality_mean_spectrum(n, N) + self.assertAlmostEqual(uniform, 1.0, places=13) + self.assertAlmostEqual(orthogonal, 0.0, places=13) + + def test_exact_small_ensemble_mean_matrix(self) -> None: + n, m = 4, 3 + N = 1 << n + matrices = [] + for support in combinations(range(N), m): + c = matrix_from_support(n, support) + matrices.append(c.T @ c) + empirical = np.mean(matrices, axis=0) + uniform, orthogonal = fixed_cardinality_mean_spectrum(n, m) + d = 1 << (n // 2) + analytic = orthogonal * np.eye(d) + (uniform - orthogonal) * np.ones((d, d)) / d + np.testing.assert_allclose(empirical, analytic, rtol=0, atol=2e-14) + + +class ApproximationTests(unittest.TestCase): + def test_hypergeometric_diagonal_entropy_against_enumeration(self) -> None: + n, m = 4, 3 + N = 1 << n + entropies = [] + for support in combinations(range(N), m): + c = matrix_from_support(n, support) + diagonal = np.diag(c.T @ c) + positive = diagonal[diagonal > 0] + entropies.append(float(-np.sum(positive * np.log2(positive)))) + exact_average = float(np.mean(entropies)) + formula = hypergeometric_occupancy_approximation(n, m) + self.assertAlmostEqual(formula, exact_average, places=13) + + def test_dense_approximation_is_finite_and_has_full_support_endpoint(self) -> None: + for n in (4, 8, 14): + N = 1 << n + for m in (1, max(2, N // 20), max(2, N // 3), N): + self.assertTrue(np.isfinite(dense_bulk_approximation(n, m))) + self.assertEqual(dense_bulk_approximation(n, N), 0.0) + + +class QFTConventionTests(unittest.TestCase): + def test_positive_exponent_qft(self) -> None: + n = 4 + N = 1 << n + support = np.asarray([0, 1, 3, 8], dtype=int) + state = np.zeros(N, dtype=complex) + state[support] = 1 / np.sqrt(len(support)) + j = np.arange(N) + direct = np.exp(2j * np.pi * np.outer(j, j) / N) @ state / np.sqrt(N) + computed = qft_state_from_support(n, support) + np.testing.assert_allclose(computed, direct, rtol=0, atol=2e-14) + + def test_fourier_sign_does_not_change_entropy_for_real_input(self) -> None: + n = 4 + N = 1 << n + support = np.asarray([0, 2, 5, 7, 10], dtype=int) + state = np.zeros(N, dtype=complex) + state[support] = 1 / np.sqrt(len(support)) + positive = np.fft.ifft(state, norm="ortho") + negative = np.fft.fft(state, norm="ortho") + self.assertAlmostEqual( + entropy_from_state_vector(n, positive), + entropy_from_state_vector(n, negative), + places=13, + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_exact_purity_and_residue.py b/tests/test_exact_purity_and_residue.py new file mode 100644 index 0000000..c984601 --- /dev/null +++ b/tests/test_exact_purity_and_residue.py @@ -0,0 +1,35 @@ +from __future__ import annotations +from itertools import combinations +import unittest +import numpy as np +from subset_states.core import ( + entropy_from_support, + fixed_cardinality_average_purity, + matrix_from_support, + residue_class_entropy_ceiling, +) + +class ExactPurityTests(unittest.TestCase): + def test_exhaustive_n4_average_purity(self) -> None: + n = 4 + N = 1 << n + for m in range(1, N + 1): + purities = [] + for support in combinations(range(N), m): + c = matrix_from_support(n, support) + rho = c.T @ c + purities.append(float(np.trace(rho @ rho))) + self.assertAlmostEqual(np.mean(purities), fixed_cardinality_average_purity(n, m), places=12) + +class ResidueCeilingTests(unittest.TestCase): + def test_exhaustive_n4_ceiling(self) -> None: + n = 4 + N = 1 << n + for mask in range(1, 1 << N): + support = np.asarray([x for x in range(N) if mask >> x & 1], dtype=np.int64) + entropy = entropy_from_support(n, support) + for t in (1, 2): + self.assertLessEqual(entropy, residue_class_entropy_ceiling(n, support, t) + 2e-12) + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_table_i.py b/tests/test_table_i.py new file mode 100644 index 0000000..91c6163 --- /dev/null +++ b/tests/test_table_i.py @@ -0,0 +1,32 @@ +from __future__ import annotations + +import unittest +import numpy as np + +from subset_states.tables import table_i_array + + +class TableIScalingTests(unittest.TestCase): + def test_full_range_regressions_unchanged(self) -> None: + table = table_i_array() + n, M, S = table[:, 0], table[:, 1], table[:, 2] + slope_M, intercept_M = np.polyfit(n, np.log2(M), 1) + slope_S, intercept_S = np.polyfit(n, S, 1) + self.assertAlmostEqual(slope_M, 0.7035409513877944, places=9) + self.assertAlmostEqual(intercept_M, -0.35773436814817483, places=9) + self.assertAlmostEqual(slope_S, 0.5093, places=9) + self.assertAlmostEqual(intercept_S, -0.9900909091, places=9) + + def test_low_n_robustness_comparison(self) -> None: + table = table_i_array() + low = table[table[:, 0] <= 20] + slope_M_low = np.polyfit(low[:, 0], np.log2(low[:, 1]), 1)[0] + slope_S_low = np.polyfit(low[:, 0], low[:, 2], 1)[0] + slope_M_full = np.polyfit(table[:, 0], np.log2(table[:, 1]), 1)[0] + slope_S_full = np.polyfit(table[:, 0], table[:, 2], 1)[0] + self.assertLess(abs(slope_M_low - slope_M_full) / abs(slope_M_full), 0.02) + self.assertLess(abs(slope_S_low - slope_S_full) / abs(slope_S_full), 0.02) + + +if __name__ == "__main__": + unittest.main() diff --git a/validation/FINAL_SCIENTIFIC_VALIDATION.txt b/validation/FINAL_SCIENTIFIC_VALIDATION.txt new file mode 100644 index 0000000..a94227e --- /dev/null +++ b/validation/FINAL_SCIENTIFIC_VALIDATION.txt @@ -0,0 +1,35 @@ +FINAL SCIENTIFIC VALIDATION +============================= + +exhaustive_n4 +------------- +supports_enumerated: 65535 +max_mean_rho_error: 2.067790383364354e-14 +max_average_purity_error: 8.881784197001252e-16 +max_residue_bound_violation_t1: 0 +max_residue_bound_violation_t2: -0 +max_entropy_routine_difference: 5.551115123125783e-16 + +table_fits +---------- +S_slope: 0.5093 +S_intercept: -0.9900909090909144 +log2M_slope: 0.7035409513877944 +log2M_intercept: -0.3577343681481748 +page_gap_n10: 0.207474201201169 +page_gap_n30: 0.01565248033929123 +support_fraction_n10: 0.1044921875 +support_fraction_n30: 0.00171054620295763 + +dense_ansatz +------------ +max_old_new_difference: 2.664535259100376e-15 + +residue_controls +---------------- +max_residue_claim_rounding_error: 3.951718681866057e-07 +prime_parity_ceiling_bits: 6.006491631063628 +prime_forced_gap_bits: 0.9935083689363715 +all_six_strongest_controls_below_all_1000_nulls: 1 + +STATUS: PASS diff --git a/validation/REFERENCE_FINAL_SCIENTIFIC_VALIDATION.txt b/validation/REFERENCE_FINAL_SCIENTIFIC_VALIDATION.txt new file mode 100644 index 0000000..a94227e --- /dev/null +++ b/validation/REFERENCE_FINAL_SCIENTIFIC_VALIDATION.txt @@ -0,0 +1,35 @@ +FINAL SCIENTIFIC VALIDATION +============================= + +exhaustive_n4 +------------- +supports_enumerated: 65535 +max_mean_rho_error: 2.067790383364354e-14 +max_average_purity_error: 8.881784197001252e-16 +max_residue_bound_violation_t1: 0 +max_residue_bound_violation_t2: -0 +max_entropy_routine_difference: 5.551115123125783e-16 + +table_fits +---------- +S_slope: 0.5093 +S_intercept: -0.9900909090909144 +log2M_slope: 0.7035409513877944 +log2M_intercept: -0.3577343681481748 +page_gap_n10: 0.207474201201169 +page_gap_n30: 0.01565248033929123 +support_fraction_n10: 0.1044921875 +support_fraction_n30: 0.00171054620295763 + +dense_ansatz +------------ +max_old_new_difference: 2.664535259100376e-15 + +residue_controls +---------------- +max_residue_claim_rounding_error: 3.951718681866057e-07 +prime_parity_ceiling_bits: 6.006491631063628 +prime_forced_gap_bits: 0.9935083689363715 +all_six_strongest_controls_below_all_1000_nulls: 1 + +STATUS: PASS diff --git a/validation/RELEASE_VALIDATION.txt b/validation/RELEASE_VALIDATION.txt new file mode 100644 index 0000000..13a1241 --- /dev/null +++ b/validation/RELEASE_VALIDATION.txt @@ -0,0 +1,17 @@ +PUBLICATION RELEASE VALIDATION +============================== + +Date: 2026-08-18 +Python: 3.13.5 + +Checks completed: +- source compilation: PASS +- unit and regression tests: PASS +- independent final scientific validation: PASS +- Figure 2 regeneration: PASS +- Figure 5 redraw from released data: PASS +- all seven final PDF figures present: PASS + +This package is an overlay release candidate. Existing historical output CSVs in +the GitHub repository should be preserved by uploading over the current branch +rather than deleting the repository contents first.