State-Dependent_Visibility_of_Non-Commutative_Ordering_in_Quantum_Dynamics

# State-Dependent Visibility of Non-Commutative Ordering in Quantum Dynamics This repository contains the numerical data and self-contained reproduction code for the manuscript *State-Dependent Visibility of Non-Commutative Ordering in Quantum Dynamics*. It includes the seven 18-qubit ground states used as inputs, the complete normalized overlap curves for every displayed operator pair, the short-time expansion data, and all 57 cases in the coefficient-robustness study. The release separates immutable manuscript data under `data/` from newly computed outputs under `reproduced/`. Reproduction commands therefore do not overwrite the published data unless paths are changed manually. ## Scientific definition For each Hermitian operator pair (B,C), define \[ A_1=B+iC,\qquad A_2=B-iC,\qquad M=A_1A_2,\qquad \widetilde M=A_2A_1. \] The released curves contain \[ F_\psi(\tau)=\left|\langle\psi| e^{+i\widetilde M\tau}e^{-iM\tau}|\psi\rangle\right|, \qquad u=\Omega\tau, \qquad \Omega=\|M\|_{\mathrm{op}}. \] The window visibility reported in the manuscript is \[ \mathcal V_\psi(U)=1-\min_{0\le u\le U}F_\psi(u/\Omega). \] All full manuscript curves use (u=0:0.0025:20), followed by exact local refinement of every coarse-grid minimum. Pair A is evaluated in all seven ground states; pairs B-I are evaluated in the two endpoint states. Thus `manuscript_pair_curves.jsonl` contains exactly 23 pair/state curves. ## Repository layout ```text State-Dependent_Visibility_of_Non-Commutative_Ordering_in_Quantum_Dynamics/ |-- README.md |-- CITATION.cff |-- requirements.txt |-- reproduce.py |-- data/ | |-- data_manifest.json | |-- operator_pairs.json | |-- ground_states/ | | |-- gs_lam_0.05.npz ... gs_lam_3.20.npz | | `-- source_manifest.json | `-- manuscript_results/ | |-- manuscript_pair_curves.jsonl | |-- representative_normalized_curves.json | |-- top_family_normalized.jsonl | |-- short_time_moments.json | |-- echo_series.json | |-- coefficient_robustness_corrected.jsonl | |-- coefficient_robustness_corrected_summary.json | |-- normalization_audit.json | |-- state_audit.json | `-- provenance_summary.json |-- scripts/ | |-- reproduce_ground_states.py | |-- reproduce_visibility.py | |-- reproduce_short_time.py | |-- reproduce_robustness.py | |-- reproduce_figures.py | |-- verify_release.py | `-- prepare_release_data.py |-- src/ | |-- hamiltonian.py | |-- lattice.py | |-- pauli_algebra.py | |-- operators.py | |-- observable.py | |-- utils.py | `-- visibility.py `-- tests/test_core.py ``` ## Environment Python 3.11 or newer is recommended. The frozen production records report Python 3.13.2, NumPy 2.4.4, and SciPy 1.17.1. Install the public dependencies with: ```bash python -m venv .venv python -m pip install --upgrade pip python -m pip install -r requirements.txt ``` On PowerShell, activate the environment with `.\.venv\Scripts\Activate.ps1`; on POSIX shells use `source .venv/bin/activate`. ## Verify the release The fast verification checks every published file against `data/data_manifest.json`, validates all state shapes and norms, verifies the A-I operator hashes and pair/state coverage, and checks the manuscript's short-time and robustness invariants: ```bash python reproduce.py verify python -m unittest discover -s tests -v ``` To additionally rebuild all seven sparse Hamiltonians and evaluate every ground state residual, run: ```bash python reproduce.py verify --deep ``` ## Reproduce the ground states The Hamiltonian is the periodic (3\times3), 18-link model \[ H(\lambda)=-\sum_p P_p^Z-\lambda\sum_{\ell=0}^{17}X_\ell, \] with link indices \[ q(h_{i,j})=6i+2j,\qquad q(v_{i,j})=6i+2j+1. \] Qubit 0 is the least-significant bit of the computational-basis index. Recompute all seven states with a deterministic positive starting vector for `eigsh`: ```bash python reproduce.py ground-states ``` Outputs are written to `reproduced/ground_states/`. Sparse eigensolver vectors may differ by a global phase and by small platform-dependent roundoff. Compare states by absolute overlap and Hamiltonian residual, not byte identity. ## Reproduce all B,C curves The following command recomputes pair A at all seven values ```text lambda = 0.05, 0.10, 0.20, 0.40, 0.80, 1.60, 3.20 ``` and pairs B-I at `lambda=0.05` and `3.20`: ```bash python reproduce.py visibility --workers 4 ``` The result is written to `reproduced/visibility/`. Each JSONL record stores the full `u_grid`, physical `tau_grid`, (F_\psi), (Omega), refined minima, (\mathcal V(U)), average visibility, pair signature, state checksum, and active subspace size. To reproduce only selected pairs, invoke the script directly: ```bash python scripts/reproduce_visibility.py --pairs A E H --workers 3 ``` By default, numerical scripts read the immutable states in `data/ground_states/`. Use `--state-dir reproduced/ground_states` to propagate newly recomputed states through a later stage. The unified `all` command sets this option automatically. Run a short end-to-end computation before committing substantial resources: ```bash python reproduce.py visibility --quick --workers 1 --force ``` The quick profile uses (u=0:0.05:1) and is a code-path test, not manuscript precision. ## Short-time and robustness data Recompute the order-10 overlap series, commutator moments, and exact short-time validation for pair A: ```bash python reproduce.py short-time ``` Recompute the base case, 16 one-at-a-time coefficient changes, and 40 seeded simultaneous random changes: ```bash python reproduce.py robustness --workers 4 ``` The random cases use NumPy `PCG64` with seeds `20260730` for `sigma=0.05` and `20260731` for `sigma=0.10`. The robustness calculation is the most expensive workflow and checkpoints completed cases. Its smoke profile is: ```bash python reproduce.py robustness --quick --workers 1 --force ``` ## Figures and complete workflow Generate the nine vector PDF figures from the frozen data: ```bash python reproduce.py figures ``` They are written to `reproduced/figures/`. To run every full numerical stage and then generate figures: ```bash python reproduce.py all --workers 4 ``` This full command requires substantial CPU time and memory. The visibility code uses sparse active-subspace propagation in chunks of 16 time steps; the largest displayed pair has 15 active qubits. ## Data formats `data/operator_pairs.json` is the authoritative human-readable A-I table. An operator signature has the form `[B_terms, C_terms]`; each term is `[real_weight, [[qubit_index, Pauli_letter], ...]]`. It also records the notation used in the manuscript, active support (k), operator hash, and evaluated states. Ground-state NPZ files always contain `state`. The endpoint files additionally retain their historical `energy` and `lam` arrays; intermediate frozen files do not. Recomputed files contain all three keys. `state_audit.json` supplies energies and residuals for every frozen state. The two original production curve files are retained for provenance. The derived `manuscript_pair_curves.jsonl` removes the symmetry-related tenth search output and combines the A-I records actually used in the manuscript. It is generated deterministically by `scripts/prepare_release_data.py` without changing any floating-point values. `data/data_manifest.json` records each data file's byte size, SHA-256 checksum, and, where applicable, NPZ array metadata or JSONL record count. ## License The code and data in this repository are released under the Apache License 2.0. See `LICENSE` for the complete terms.