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Python Scripts

Shared utilities

gf2.py

Shared library module (not executable). Provides GF(2) linear algebra: matrix inversion, rank computation, Gauss-Jordan elimination (Numba-accelerated). Also includes tensor I/O helpers, basis change application, and bitvector decoding.

Used by: make_cpd_gf.py, verify_paper_schemes.py, collect_paper_schemes.py.

Requires: numpy, numba.

Tensor generation

make_tensors_gfmult.py

Generates GF(2^k) multiplication tensors for k = 2..10 in three representations:

Series Dims Description
03xx (k, k, 2k-1) Polynomial multiplication (convolution)
05xx (k, k, k) GF(2^k) multiplication mod irreducible polynomial
07xx (3k, 3k, 3k) Phase tensor (topp embedding of 05xx)

Outputs 27 tensors to data/tensors/ (IDs 0325-0333, 0525-0533, 0725-0733). Uses hardcoded primitive polynomials; no external input needed.

make_cpd_gf.py

Constructs known-rank CP decompositions for GF(2^k) multiplication tensors (k = 2..10) using algebraic tower-field decompositions with explicit isomorphisms.

Outputs to data/cpd/base/ and data/cpd/topp/. Optionally verifies against pre-existing tensors in data/tensors/.

make_rnd_bench.py

Generates 512 planted random benchmark tensors with known CP rank (ground truth). Parameters: 8 dimensions (6, 8, ..., 20) × 16 ranks (1..16) × 4 repetitions.

Outputs tensors (IDs 2000-2511) to data/tensors/ and ground-truth CPD files to data/other/cpd-rnd/topp/.

Note: Uses random generation; re-running produces different tensors. Pre-generated tensors are included in the repository.

Circuit import

setup_circuits_atq.py

Imports AlphaTensor-Quantum benchmark circuits. Clones the alphatensor_quantum repo, reconstructs symmetric tensors from Waring decomposition factors.

Outputs 66 tensors (IDs 0101-0168) to data/tensors/.

Requires: git, internet access.

setup_circuits_todd.py

Imports quantum circuits from the quantum-circuit-optimization repository. Copies .qc files to data/circuits/raw/ with numeric IDs, optionally compiles them to extract phase polynomials and tensors.

Outputs .qc files and tensors (IDs 0800-0876) to data/circuits/raw/ and data/tensors/.

Requires: git, internet access. Optional: bin/compile (for tensor extraction).

Verification

verify_paper_schemes.py

Verifies all CP and Waring decompositions in data/paper/ against original tensors. For each tensor, loads the BCO transform, reconstructs the dense tensor from the decomposition, and checks it matches the original.

Reads from data/tensors/, data/paper/transform/, data/paper/cpd/topp/, data/paper/waring/. Prints PASS/FAIL for each tensor; exits with status 1 on any failure.

Internal (not needed for reproduction)

collect_paper_schemes.py

Collects best optimization results from data/tmp/ncgm02/ (intermediate experimental output) into data/paper/. This is an internal script used during paper preparation — the collected results are already included in the repository.