Verifiable Quantum Circuit Compilation — Optimized Submission Bundle

Complete, self-contained bundle for the Kaggle competition Google — Verifiable Quantum Circuit Compilation (competition 161954): optimized circuits for all three benchmarks, the builders that produce them, the official verifiers, and the recorded verification evidence.

Cost model (all three benchmarks): score = Q² × T, where Q = peak qubits and T = Toffoli count. Lower is better.

Headline results

Baselines are the competition sample submission. DQI note: relative to the pre-session submission (20,679,670,765,943.19), the DQI improvement is −14.5%; the −27.7% figure is against the sample-submission baseline.

All three circuits PASS the official verifiers with zero value errors and zero phase errors (see verification/ and docs/REPRODUCING.md).

What to submit

Upload the contents of submission/ (not this README tree) as the competition submission:

submission/
├── invsqrt.kmb          Benchmark I circuit (684,969.09)
├── dqi.kmb              Benchmark II circuit (17,673,729,048,937.30)
├── dfthcsos/
│   ├── angle_k_0.kmb … angle_k_6.kmb
│   └── submission.npz
└── README.md            submission notes (methods + scores)

Bundle layout

Quick start

source ./env.sh                          # Linux x86_64, Python 3.13, numpy+scipy
"$PYTHON_BIN" builders/test_gf_primitives.py   # exhaustive GF(2^12) primitive tests
"$PYTHON_BIN" verifiers/dqi/verify_submission_dqi.py submission/dqi.kmb

Full instructions: docs/REPRODUCING.md.

Methods in one paragraph each

• I. Inverse square root — replaces the 4-step Newton iteration with a finite-difference tail-polynomial evaluated at a doubled Newton root, screened by exhaustive search over shift/scaled-e₂ recurrences at the 24-bit exactness boundary. 89 qubits, 1,670 Toffolis.
• II. DQI — composite-tower GF(2¹²) arithmetic: the field inverse is built as GF((2³)²) towers with generated bilinear multiplies (54 products for GF(2¹²), 18 for GF(2⁶), 6 for GF(2³)), Toffoli-free measurement-style erasure, in-place basis changes, narrowed degree counters, and an 11-Toffoli AND-tree σ=0 test in the Chien search.
• III. DFTHC-SOS — symmetry-verified sum-of-squares factorization of the FeMoCo Hamiltonian with Clifford-only Givens words compiled from permutation/phase tables; selected by full spectral certificates.

Details: docs/METHODS.md. Inspiration (public Kaggle portfolio notebooks on measurement-based cleanup and shared-product uncomputation) and rejected approaches are documented in docs/DESIGN_NOTES.md.

Provenance & licensing

• Circuits, builders, tests, and documentation in this bundle: original work from the optimization sessions, released under CC0-1.0.
• verifiers/, kickmix/, and score.py originate from the competition organizers and are redistributed under their Apache-2.0 licenses (verifiers/LICENSE.txt, kickmix/LICENSE.txt) for reproducibility.

Integrity

MANIFEST.sha256 lists the SHA-256 of every bundled file, including the submission circuits, so any copy can be checked byte-for-byte against the verified artifacts recorded in verification/.