| # Optimization decision — Verifiable Quantum Circuit Compilation |
|
|
| Date: 2026-11-07. Status: decision made from verified baselines; first measurement in progress. |
| Author: xI, from three read-only surveys (paper + scoring docs, Google Drive, GitHub). |
|
|
| ## 0. What we know for certain |
|
|
| Scoring: overall score = geometric mean of `baseline_cost / submitted_cost` across |
| the three tasks; reference submission scores 1.0 by construction; any failing task |
| rejects the whole submission. (Kaggle rules, not the paper — the paper defines only |
| per-task scores.) A 2x improvement on any one task is worth exactly as much as 2x on |
| any other. There is no benefit to over-optimizing one task. |
|
|
| Verified baselines (Nov 7, 2026): |
|
|
| | Task | Baseline score | Verified by | Q | Dominant cost | |
| |---|---|---|---|---| |
| | dfthcsos | 3,355,599,588.32 | local full run, exact README match | 730 | ANGLES QROM 85% of Toffolis; λ_eff = 49.301369 multiplies everything | |
| | invsqrt | 2,068,518.26 sampled (paper full-run 2.08e6) | local sampled run x=1..1024 | 260 | ~7,735 Toffolis + 37 rotations; worst error only ~2.1x inside tolerance | |
| | DQI | 24,439,463,583,672.93 | Kaggle notebook, full 102,400 shots, 0 errors | 1,893 | 5.7M Toffolis; Q^2 weighting; per-position inversion ~25% of Toffolis | |
| |
| The organizers commit SHA-256 hashes of their own best internal runs (paper p.7) and |
| say AI agents already found "significant improvements over the previously published |
| baselines" — but publish no numbers. The true bar above the reference baselines is |
| unknown. Assume the reference is not the bar. |
| |
| **The bar is now measured (2026-11-07, public Kaggle notebooks): the field is at |
| ~25x the reference geometric mean.** Public notebooks show LB 24.94 ("Verified |
| Three-Task Portfolio") and best 24.87 ("The Unbearable Lightness of Quantum |
| Circuits"); a participant repo read Nov 2 put the leader at ~28.0. What the field |
| did, per those notebooks: DQI rebuilt at 892 qubits (vs 1,893 reference — the Q^2 |
| lever, exactly as §1 predicts), chemistry refit with a (9, 143, 40) |
| factorization, invsqrt at 62 qubits (vs 260). So to be competitive, roughly 3x |
| per task (3^3 ≈ 27) is the scale of improvement needed — not 10%. The levers in |
| §1 are confirmed by the field; the work is execution, not discovery. |
| |
| ## 1. Where the headroom is (inference from the paper) |
| |
| **dfthcsos — λ_eff is a straight multiplier.** Score = λ_eff x T_total x Q_total. |
| λ_eff = sqrt(E_gap(2Λ - E_gap)); the baseline's 12-bit quantization costs only ~0.1% |
| of λ_eff, so the factorization itself is the lever: better (R,B,C) rank allocation and |
| better-optimized vectors (u, w, W) flow straight through, subject to ε_fro ≤ 20 mHa |
| and the floors Λ > 49.0 Ha, E_gap > 3.914898 Ha. This is a *classical numerical |
| optimization* (the dfthc-sos starter kit's trainer), not a circuit problem — it can |
| be iterated locally with fast verification (~25 s per verify). |
|
|
| **DQI — qubits pay quadratically.** Score = R(ε+) x Q^2 x T. 2(n+3)b = 1,752 of the |
| 1,893 qubits are the two EEA polynomial arrays. A 1% qubit cut is worth a 2% Toffoli |
| cut. Second lever: the per-position Itoh-Tsujii inversion, ~1.44M Toffolis (~25%), |
| which the paper says "can be improved" — batch inversion (Montgomery's trick) is our |
| inference, not paper-named. Third: GF(2^12) multiplier 63 → 51 Toffolis is |
| demonstrated in the literature (Ref. [12]), ~0.5M Toffolis. Fourth, paper-endorsed: |
| deliberate approximation — ε+ = 1e-3 costs only R = 1.21 vs the 1.19 floor, so a |
| rarely-failing but much cheaper decoder can beat an exact one. This is the biggest |
| prize and the slowest loop (full verify = 201 s on a Kaggle notebook; not runnable |
| at full scale on this 8 GB VM). |
|
|
| **invsqrt — polynomial and bit-widths.** Score = Q x C, C = Toffolis + T/4. The paper |
| names the central tradeoff directly: cubic polynomial over a small rescaled range vs |
| a simpler polynomial over a larger range; coefficient accuracy from QROM; "a |
| completely different route… simply finding a good polynomial approximation over the |
| input domain." Bit-widths (14/17/28/28/29) were tuned for worst error 2.84e-8, ~2.1x |
| inside the 2^-24 tolerance — narrower widths cut the big 28-bit multipliers but eat |
| the rotation margin, since rotation T-cost is priced by leftover margin. Fastest |
| local loop (sampled verify), but full verify is 200.5M shots — sampled only, locally. |
|
|
| ## 2. The decision |
|
|
| **First: dfthcsos.** Reasons, in order: |
| 1. λ_eff is a direct multiplier on the whole task score, and the lever is classical |
| numerical optimization — no new circuit construction, no verifier risk beyond |
| the two error floors. |
| 2. Fastest verification loop of the three at full scale (~25 s, local). |
| 3. The brot/rank sweep is measurable before any commitment: `evaluate_words` gives |
| error_1/error_2 vs brot and rank, so the first experiment either confirms or |
| kills the headroom in minutes. |
|
|
| **Second: invsqrt.** Fast sampled loop locally; polynomial redesign is paper-invited |
| and the 2.1x error margin is the measurable constraint. Risk: full verification is |
| 200M shots, so any candidate needs a Kaggle-scale final check. |
|
|
| **Third: DQI.** Largest absolute prize (Q^2 + 25% inversion block + demonstrated |
| 51-Toffoli multiplier), but the slowest loop and the biggest circuit (86M |
| instructions). Attack it after the other two have a verified pipeline, using the |
| Kaggle notebook for full verification. Do not start here — iteration cost would |
| dominate the work. |
|
|
| ## 3. What the surveys found (and did not) |
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|
| - **Google Drive:** nothing directly relevant. No kickmix/dfthcsos/FeMoCo/Qualtran |
| hits; no prior optimization plan. Tangential only: a CUDA-Q kernel optimization |
| notebook (Oct 4, 2026) and GTX 1650 optimization notes (May 11, 2026) — different |
| framework, background only. The optimization starts from local material. |
| - **GitHub:** no igor-holt repo for this competition; local quantum-comp work is not |
| pushed anywhere. Upstream Qualtran is current (local HEAD 9a0c11a = upstream |
| latest, Nov 2). **Gap found:** the local Qualtran repo is a blobless sparse |
| checkout with only `docs/kickmix/` and `kickmix/` on disk — the `qualtran/` |
| package is not checked out and `import qualtran` fails in the venv. Fix before |
| using any bloq: `git sparse-checkout add qualtran` (or pip-install qualtran). |
| - **No optimizer exists anywhere in the stack.** Neither Qualtran nor kickmix ships |
| a circuit-optimization pass. Gains come from hand-built bloq substitutions + |
| rotation-synthesis tuning, verified with the kickmix cost counter. The building |
| blocks exist: rotation synthesis + `NewtonRaphsonApproxInverseSquareRoot` / |
| `PolynmomialEvaluationInverseSquareRoot` (invsqrt); GF/GF-poly arithmetic (DQI); |
| THC + double factorization + Givens (dfthcsos); QROM/SelectSwapQROM (angle tables). |
|
|
| ## 4. First measurement — DONE 2026-11-07 (sweep ran 161 s) |
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|
| Script + results: `dfthcsos_brot_sweep.py`, `dfthcsos_brot_sweep.json`. |
| Method: recovered the reference angle words (3,976 x 75) from the circuits with |
| the stock verifier's own simulator, re-quantized them to fewer bits by |
| round-to-nearest, re-evaluated with the stock `evaluate_words`. |
|
|
| | brot | error_1 (mHa) | error_2 (mHa) | λ_eff | verdict | |
| |---|---|---|---|---| |
| | 12 (baseline) | 3.19 | 18.64 | 49.301 | PASS; score reproduced exactly: 3,355,599,588.32 | |
| | 11 | 76.95 | 29.80 | 49.395 | REJECTED — both errors over 20 mHa | |
| | 10 | 134.85 | 44.89 | 49.626 | REJECTED | |
| | 9 | 273.48 | 83.77 | 50.969 | REJECTED | |
| | 8 | 590.54 | 172.44 | 55.454 | REJECTED | |
| | 7 | 1,328.67 | 349.00 | 66.056 | REJECTED | |
| | 6 | 3,078.97 | 729.04 | 93.243 | REJECTED | |
| |
| Two findings that change the plan: |
| 1. **Naive bit reduction is dead.** One bit less (12 → 11) blows error_1 from |
| 3.19 to 76.95 mHa — 4x over the bound. Lower brot also *raises* λ_eff |
| (E_gap grows with quantization error), so there is no tradeoff to rescue. |
| (The numerically lower "scores" at brot 11/10 in the JSON are meaningless: |
| those submissions are rejected, score = ∞.) |
| 2. **The baseline is already near the two-body bound.** error_2 = 18.64 mHa |
| leaves only 1.36 mHa of headroom under 20 mHa. Any rank reduction or |
| re-quantization must be paired with re-optimization of the vectors — the |
| factorization has almost no slack to spend. |
| |
| Revised first lever: **factorization refit, not rounding.** Re-optimize the |
| vectors/weights (U, w, W) to minimize λ_eff subject to ε_fro ≤ 20 mHa, at |
| brot=12 — or quantization-aware vectors for brot=11. The metrics function |
| (`evaluate_dfthc_angle_words`) and the baseline factorization are both local, |
| so this is a classical scipy optimization; the dfthc-sos starter kit trainer |
| is not in the downloaded dataset (it lives in a separate starter-kit dataset |
| named in SCORING_README.md) and is not strictly required. |
| |
| ## 5. Verification discipline |
| |
| - Every candidate is verified with the stock verifier before it counts. No |
| hand-waved cost claims. |
| - dfthcsos: local full verify (~25 s). invsqrt: sampled locally, full on Kaggle. |
| DQI: full on Kaggle notebook only (201 s, 4 workers). |
| - Nothing is submitted to the competition without Igor's explicit go-ahead. |
| Nothing is published from a Kaggle notebook without his say-so. |
| - Per-stage Toffoli splits for invsqrt/DQI (marks exist in the reference builders) |
| are still unmeasured — extract before optimizing either circuit's internals. |
| |
| ## 6. Open / unconfirmed |
| |
| - Exact overall geometric-mean formula (Kaggle rules, not paper). |
| - Organizers' internal best-run scores (hashes only). |
| - dfthcsos error_1/error_2 of the baseline (being measured now). |
| - Whether brot reduction keeps error_1/error_2 under 20 mHa (sweep will tell). |
| - Per-stage Toffoli splits for invsqrt and DQI. |
| |
