A research-grade, six-week masterclass on the mathematics and practice of quantum computing for machine learning, built from first principles. In the spirit of building understanding from the ground up, the course begins with pure NumPy: qubits are complex vectors, gates are unitary matrices, and measurement is the Born rule applied by hand. Once the mechanics are transparent, the course bridges to PennyLane, a production quantum-machine-learning framework with automatic differentiation, so that the same concepts scale to real variational algorithms and hardware back-ends.
The goal is not to take quantum software on faith. By the end, a reader will have implemented a state-vector simulator, the canonical quantum algorithms (Deutsch–Jozsa, Grover, the quantum Fourier transform), and a complete variational quantum classifier and quantum-kernel method — understanding each at the level of the underlying linear algebra, and able to read a quantum-machine-learning paper and reproduce its core experiment.
The material assumes comfort with linear algebra (complex vector spaces, inner products, eigendecomposition, tensor/Kronecker products), basic probability, and Python with NumPy. Prior exposure to classical machine learning (gradient descent, classifiers, kernels) is helpful for the second half but is reintroduced from the quantum viewpoint where needed. No prior quantum physics is required — the postulates are developed from scratch.
The course spans six weeks in three movements.
Part I — Quantum foundations (Weeks 1–2). The qubit as a complex unit vector, single- and multi-qubit gates as unitaries, superposition, the Born rule for measurement, entanglement, and the Bell states — all implemented as a from-scratch state-vector simulator.
Part II — Quantum algorithms (Weeks 3–4). The oracle/query model and quantum parallelism through Deutsch–Jozsa; amplitude amplification in Grover search; the quantum Fourier transform; and the crossover to variational circuits and the parameter-shift rule, where quantum computing meets optimization. This is where we bridge to PennyLane.
Part III — Quantum machine learning (Weeks 5–6). Variational quantum classifiers and data encoding (the feature map), the role of expressivity and barren plateaus, quantum kernel methods, and a capstone comparing quantum and classical models on a shared task.
| Week | Notebook | Topic |
|---|---|---|
| 1 | 01_qubits_states_gates.ipynb |
Qubits, the Bloch sphere, single-qubit gates, a from-scratch simulator |
| 2 | 02_entanglement_measurement.ipynb |
Multi-qubit states, tensor products, measurement, Bell states, CHSH |
| 3 | 03_quantum_algorithms.ipynb |
Oracles, Deutsch–Jozsa, Grover search, the quantum Fourier transform |
| 4 | 04_variational_circuits_pennylane.ipynb |
Parameter-shift rule, VQE, the bridge to PennyLane |
| 5 | 05_quantum_machine_learning.ipynb |
Data encoding, variational quantum classifiers, training and barren plateaus |
| 6 | 06_quantum_kernels_capstone.ipynb |
Quantum kernels, quantum vs classical comparison, capstone project |
Each notebook is self-contained: it develops the theory with full derivations, implements the method from scratch (and/or in PennyLane), validates it against analytical results, and closes with graded exercises.
Part I and the algorithmic core of Part II use NumPy only, so the reader sees every amplitude and
every unitary. Where variational training and automatic differentiation are essential — the
parameter-shift rule, VQE, quantum classifiers, quantum kernels — the course uses PennyLane with
its default.qubit simulator. The PennyLane circuits are written to mirror the from-scratch
implementations, making the bridge explicit.
git clone <repository-url>
cd quantum_artificial_intelligence
python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt
jupyter labOpen the notebooks in order; later weeks build on the simulator and intuitions established earlier.
Released for educational use. See repository settings for the applicable license.