[WIP] Add fermionic support to belief-propagation simple update#155
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[WIP] Add fermionic support to belief-propagation simple update#155mtfishman wants to merge 7 commits into
mtfishman wants to merge 7 commits into
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Keep belief-propagation messages as operators and normalize them by their trace rather than an entrywise sum, which stays sign correct on fermionic bonds where the entrywise sum can flip the odd-parity block. Gauge the simple-update tensors with the balanced square root and inverse square root of the Hermitian-projected bond messages. Depends on the operator-form Hermitian factorizations added in the ITensorBase mf/operator-sqrth branch.
The BP simple-update gauge absorbs an operator-valued square root of each incoming message into the state tensor. Contracting it with `*` returns an operator, so the updated state is written back as an operator and rejected by the state network. Take the underlying tensor of each gauge (`ITB.state`) before contracting, so the gauged state stays a plain tensor while the index arrows still carry the fermion sign. Requires the operator `dimnametype` fix from ITensor/ITensorBase.jl#225. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Store both directed messages of a bond uniformly as the bond (ket output) and an auxiliary leg (bra input), with conj(S)/S into the two endpoints, and build the initial identity messages on the source-side ket axis so their ket leg is dual to the destination bond. The gauge projects the message Hermitian and takes the balanced square-root / inverse-square-root in whichever bipartition is positive semidefinite, which recovers the odd-parity fermion sign in both directions. Migrate the message-update path to the ITensorBase 0.13 outputnames/inputnames API and bump to 0.9.10.
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## main #155 +/- ##
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- Coverage 84.89% 0.00% -84.90%
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Files 15 13 -2
Lines 662 636 -26
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- Misses 100 636 +536
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Replace the try/catch PSD-bipartition selection in `message_gauge` with a plain transposed gauge. The two directed bond messages are now built from the PSD singular-value message `conj(S)`. The reverse direction is its arrow flip via `dualize`, which toggles `isdual` and keeps the odd-parity block, rather than `conj`, which negates the odd block and breaks PSD. Free-fermion validation is exact to machine precision on trees with no fallback. `dualize` is a temporary element-wise hack that pulls in a temporary `GradedArrays` dependency. Both stand in for a proper backend-agnostic duality-flip primitive. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
The reverse directed message is S with its bond orientation reversed, which is the ribbon twist of S (-1 on the odd-parity sector). Both directed messages are then positive semidefinite in the transposed gauge, so the gauge needs no fallback. This replaces the element-wise dualize helper with a name-keyed twist and twist!. Also simplify the belief-propagation message unwrap to state.(messages), relying on state being idempotent.
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…n twist Each directed simple-update message is now the doubled contraction of the gate factor with its conjugate, rather than being read off the singular-value spectrum as conj(S) and a ribbon-twisted S. The graded contraction of a factor with its conjugate carries the odd-parity fermion sign on its own, so the explicit ribbon twist (and the direct GradedArrays dependency it needed) is gone.
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Summary
Adds fermionic support to the belief-propagation simple-update apply-gate (
apply_operators). The odd-parity sign on a fermionic bond needs care in the gauge. Each directed message is built as the doubled contraction of the gate factor with its conjugate, which carries the sign, and the gauge roots each message in the bipartition where it is positive semidefinite. The bosonic path is unchanged.TODO
FermionParity) apply-gate test coverage