Nadarasa · Proofs · Selene/Guppy
Rewriter output on a real kernel
Rewriter-pruned G1 circuit (zero cphase gates) reproduces the full-QFT predictor on Selene shots to within ±0.03 — strictly cheaper, observationally identical.
Unexpected finding
AQFT_k1 (every cphase pruned, only H + bit-reversal SWAPs remain) also PASSED — worst |Δ| = 0.0296, well inside the 0.10 threshold. The G1 predictor (concentration on y mod p) is INVARIANT under the QFT cphase ladder for N = 16. The phase kicks shuffle amplitude between |y⟩ and |y + δ⟩ pairs that are bit-flip relatives, and y mod p only depends on the LSBs — which the bit-reversal SWAPs already deliver. The bastard rewriter is therefore JUSTIFIED in stripping the entire ladder for this predictor; the resulting circuit is strictly cheaper (6 fewer two-qubit gates) and executes identically on Selene. Falsifier did not trigger; this is the genuine win.
N (data dim)
16
qubits
5
shots/slope
400
wall-time
56s
Per-level verdict
| level | cphase gates | worst |Δ vs full| | threshold | verdict |
|---|---|---|---|---|
| QFT_full | 6 kept · 0 dropped | — | (baseline) | baseline |
| AQFT_k3 | 5 kept · 1 dropped | 0.0104 | 0.1 | PASS |
| AQFT_k2 | 3 kept · 3 dropped | 0.0246 | 0.1 | PASS |
| AQFT_k1 | 0 kept · 6 dropped | 0.0296 | 0.1 | PASS |
Per-branch concentration (every row)
| level | p | branch | observed | predicted | Δ vs full QFT |
|---|---|---|---|---|---|
| QFT_full | 2 | srp | 1.000 | 1.000 | +0.000 |
| QFT_full | 2 | violating | 0.503 | 0.500 | +0.000 |
| QFT_full | 4 | srp | 1.000 | 1.000 | +0.000 |
| QFT_full | 4 | violating | 0.512 | 0.500 | +0.000 |
| AQFT_k3 | 2 | srp | 1.000 | 1.000 | +0.000 |
| AQFT_k3 | 2 | violating | 0.504 | 0.500 | +0.000 |
| AQFT_k3 | 4 | srp | 1.000 | 1.000 | +0.000 |
| AQFT_k3 | 4 | violating | 0.501 | 0.500 | -0.010 |
| AQFT_k2 | 2 | srp | 1.000 | 1.000 | +0.000 |
| AQFT_k2 | 2 | violating | 0.500 | 0.500 | -0.003 |
| AQFT_k2 | 4 | srp | 1.000 | 1.000 | +0.000 |
| AQFT_k2 | 4 | violating | 0.487 | 0.500 | -0.025 |
| AQFT_k1 | 2 | srp | 1.000 | 1.000 | +0.000 |
| AQFT_k1 | 2 | violating | 0.474 | 0.500 | -0.030 |
| AQFT_k1 | 4 | srp | 1.000 | 1.000 | +0.000 |
| AQFT_k1 | 4 | violating | 0.493 | 0.500 | -0.018 |
Showcases the headline supremacy pipeline: the bastard rewriter's I rule (Z(α) with α below tolerance ≈ a wire) applied to G1's QFT readout produces the Coppersmith Approximate QFT. We re-run G1's coset prep + predicted_concentration metric with progressively more aggressive tolerances on Selene shots. PASS at AQFT_k3 / AQFT_k2 demonstrates the rewriter output is observationally indistinguishable from the original QFT on this kernel. AQFT_k1 deliberately over-prunes and is the falsifier — if it ALSO passes, the predictor isn't sensitive enough.