TFIM — Transverse-Field Ising Model with PennyLane

Course project (Quantum Computing) exploring the 1D/2D transverse-field Ising model — exact diagonalization, entanglement/central-charge scaling, an independent Jordan-Wigner cross-check, classical-shadow reconstruction, and two VQE ansätze (hardware-efficient vs. a Hamiltonian Variational Ansatz) — grounded in the official PennyLane qspin dataset.

Full write-up: report.md. Slides + speaker notes: presentation/.

Hamiltonian

H = J Σ_<i,j> σ_i^z σ_j^z + h Σ_i σ_i^x      (J = -1, ferromagnetic)

<i,j> runs over nearest-neighbour lattice bonds; h is the transverse field. The order parameter is the longitudinal magnetization ⟨|M_z|⟩. The 1D infinite chain has a quantum critical point at h/|J| = 1.

Key results

• Critical point, two independent exact routes (Suzuki-Trotter mapping to the classical 2D Ising model; Jordan-Wigner free-fermion gap) agree on g_c = 1; the Jordan-Wigner closed form matches the dataset's exact diagonalization to 1e-13–1e-15 (src/physics/jordan_wigner.py).
• Finite-size h_c(N) from the order parameter/Binder cumulant converges toward h_c=1 as N grows, faster on the closed (periodic) chain than the open one — an explicit finite-size boundary effect (src/physics/boundary_comparison.py, src/physics/finite_size_scaling.py).
• Entanglement entropy shows the area law away from criticality and the expected CFT log-scaling at the critical point; the naive Calabrese-Cardy central-charge fit is biased on the open chain (c≈0.62) by boundary operators, confirmed by refitting on the closed chain (c≈0.51, matching the Ising CFT value 1/2) (src/physics/entanglement.py).
• VQE ansatz comparison: a physics-informed Hamiltonian Variational Ansatz with warm-starting beats a generic hardware-efficient ansatz by roughly 23× median energy error at N=8, widening to ~85× at N=16 (src/ansatz/vqe_hva.py, src/ansatz/benchmark.py).
• Barren plateaus: gradient variance for the hardware-efficient ansatz decays exponentially with N; the symmetry-respecting HVA/QAOA ansatz instead grows (src/ansatz/trainability.py).
• Classical-shadow reconstruction of √⟨M_z²⟩ from the dataset's pre-simulated randomized measurements — the one NISQ-realistic, shot-noise-limited result in the project (src/physics/classical_shadow.py).

Setup

python3.12 -m venv .venv
uv pip install -r <(echo "pennylane==0.45.0 aiohttp fsspec h5py")
.venv/bin/python -m pytest tests/ -q

The qspin dataset is downloaded on first use and cached under data/ (git-ignored). To regenerate every figure and CSV from scratch:

.venv/bin/python run_all.py

Layout

• src/ — reusable Python modules, split by role:
  • core/ — dataset loader, shared plotting style, process-pool helper
  • physics/ — order parameter, entanglement/central charge, finite-size scaling, boundary comparison, 2D lattices, Jordan-Wigner, classical shadows
  • ansatz/ — VQE/QAOA ansätze, optimizer trajectories, trainability, benchmarks
• tests/ — pytest suite mirroring src/ (core/, physics/, ansatz/)
• plots/ — generated figures (PNG), referenced by both the report and the slides
• report.md — full written report
• presentation/ — slides (Typst) + speaker notes
• run_all.py — single entry point that reproduces every figure/CSV

See CLAUDE.md for full project history, physics background, and detailed status notes.