Nadarasa · Proofs · Selene/Guppy

Noise resilience of rewriter-stripped kernels

Two Selene noise families, same coset predictor on G1. For each system size we compare the full QFT cphase ladder against the rewriter-stripped AQFT_k1 (every controlled-phase pruned by the bastard I rule). Tabs below switch noise family.

Depolarizing · DepolarizingErrorModel — every gate has a chance of a random Pauli mixing the state.

Headline — PASS

Under depolarizing noise, AQFT_k1 wins or ties full QFT in 40/48 comparisons overall (34 wins · 6 ties · 8 losses) across N ∈ {16, 32, 64}. QFT_full pays for O(n²) more cphase gates while AQFT_k1 stays linear in n, so the rewriter's decoherence head-start widens at every scale-up.

N = 16 · 5 qubits · 300 shots/slope

PASS

AQFT_k1 not-worse-than QFT_full in 83% of 12 noisy cells · mean advantage +0.073

N = 32 · 6 qubits · 200 shots/slope

PASS

AQFT_k1 not-worse-than QFT_full in 83% of 12 noisy cells · mean advantage +0.083

N = 64 · 7 qubits · 150 shots/slope

PASS

AQFT_k1 not-worse-than QFT_full in 92% of 12 noisy cells · mean advantage +0.101

N = 16 · AQFT_k1 vs QFT_full · |err vs predicted|

Each row is one (noise · p · branch) cell. Lower error is better; positive advantage means AQFT_k1 wins.

noise	p	branch	QFT_full err	AQFT_k1 err	advantage	winner
ideal	2	srp	0.000	0.000	+0.000	tie
ideal	2	violating	0.012	0.001	+0.011	AQFT_k1
ideal	4	srp	0.000	0.000	+0.000	tie
ideal	4	violating	0.009	0.005	+0.004	AQFT_k1
p1q=0.005	2	srp	0.287	0.150	+0.137	AQFT_k1
p1q=0.005	2	violating	0.001	0.007	-0.006	QFT_full
p1q=0.005	4	srp	0.544	0.333	+0.211	AQFT_k1
p1q=0.005	4	violating	0.165	0.115	+0.050	AQFT_k1
p1q=0.010	2	srp	0.440	0.277	+0.163	AQFT_k1
p1q=0.010	2	violating	0.008	0.009	-0.002	QFT_full
p1q=0.010	4	srp	0.693	0.523	+0.170	AQFT_k1
p1q=0.010	4	violating	0.246	0.175	+0.071	AQFT_k1
p1q=0.020	2	srp	0.470	0.430	+0.040	AQFT_k1
p1q=0.020	2	violating	0.006	0.001	+0.005	AQFT_k1
p1q=0.020	4	srp	0.700	0.673	+0.027	AQFT_k1
p1q=0.020	4	violating	0.240	0.233	+0.007	AQFT_k1

N = 32 · AQFT_k1 vs QFT_full · |err vs predicted|

Each row is one (noise · p · branch) cell. Lower error is better; positive advantage means AQFT_k1 wins.

noise	p	branch	QFT_full err	AQFT_k1 err	advantage	winner
ideal	2	srp	0.000	0.000	+0.000	tie
ideal	2	violating	0.000	0.003	-0.003	QFT_full
ideal	4	srp	0.000	0.000	+0.000	tie
ideal	4	violating	0.013	0.003	+0.010	AQFT_k1
p1q=0.005	2	srp	0.345	0.160	+0.185	AQFT_k1
p1q=0.005	2	violating	0.002	0.029	-0.028	QFT_full
p1q=0.005	4	srp	0.595	0.335	+0.260	AQFT_k1
p1q=0.005	4	violating	0.195	0.110	+0.085	AQFT_k1
p1q=0.010	2	srp	0.420	0.265	+0.155	AQFT_k1
p1q=0.010	2	violating	0.002	0.003	-0.001	QFT_full
p1q=0.010	4	srp	0.686	0.475	+0.211	AQFT_k1
p1q=0.010	4	violating	0.208	0.147	+0.062	AQFT_k1
p1q=0.020	2	srp	0.470	0.445	+0.025	AQFT_k1
p1q=0.020	2	violating	0.007	0.002	+0.006	AQFT_k1
p1q=0.020	4	srp	0.708	0.685	+0.022	AQFT_k1
p1q=0.020	4	violating	0.231	0.223	+0.008	AQFT_k1

N = 64 · AQFT_k1 vs QFT_full · |err vs predicted|

Each row is one (noise · p · branch) cell. Lower error is better; positive advantage means AQFT_k1 wins.

noise	p	branch	QFT_full err	AQFT_k1 err	advantage	winner
ideal	2	srp	0.000	0.000	+0.000	tie
ideal	2	violating	0.031	0.032	-0.001	QFT_full
ideal	4	srp	0.000	0.000	+0.000	tie
ideal	4	violating	0.002	0.006	-0.003	QFT_full
p1q=0.005	2	srp	0.407	0.193	+0.213	AQFT_k1
p1q=0.005	2	violating	0.008	0.009	-0.001	QFT_full
p1q=0.005	4	srp	0.634	0.340	+0.294	AQFT_k1
p1q=0.005	4	violating	0.196	0.122	+0.073	AQFT_k1
p1q=0.010	2	srp	0.520	0.373	+0.147	AQFT_k1
p1q=0.010	2	violating	0.029	0.010	+0.019	AQFT_k1
p1q=0.010	4	srp	0.804	0.587	+0.218	AQFT_k1
p1q=0.010	4	violating	0.272	0.189	+0.083	AQFT_k1
p1q=0.020	2	srp	0.493	0.447	+0.047	AQFT_k1
p1q=0.020	2	violating	0.011	0.009	+0.002	AQFT_k1
p1q=0.020	4	srp	0.740	0.660	+0.080	AQFT_k1
p1q=0.020	4	violating	0.259	0.227	+0.032	AQFT_k1

Raw measurements (all N)

N	noise	kernel	p	branch	observed	predicted	\|err\|	cphase
16	ideal	QFT_full	2	srp	1.000	1.000	0.000	6 kept
16	ideal	QFT_full	2	violating	0.488	0.500	0.012	6 kept
16	ideal	QFT_full	4	srp	1.000	1.000	0.000	6 kept
16	ideal	QFT_full	4	violating	0.491	0.500	0.009	6 kept
16	ideal	AQFT_k1	2	srp	1.000	1.000	0.000	0 kept
16	ideal	AQFT_k1	2	violating	0.499	0.500	0.001	0 kept
16	ideal	AQFT_k1	4	srp	1.000	1.000	0.000	0 kept
16	ideal	AQFT_k1	4	violating	0.495	0.500	0.005	0 kept
16	p1q=0.005	QFT_full	2	srp	0.713	1.000	0.287	6 kept
16	p1q=0.005	QFT_full	2	violating	0.499	0.500	0.001	6 kept
16	p1q=0.005	QFT_full	4	srp	0.456	1.000	0.544	6 kept
16	p1q=0.005	QFT_full	4	violating	0.335	0.500	0.165	6 kept
16	p1q=0.005	AQFT_k1	2	srp	0.850	1.000	0.150	0 kept
16	p1q=0.005	AQFT_k1	2	violating	0.507	0.500	0.007	0 kept
16	p1q=0.005	AQFT_k1	4	srp	0.667	1.000	0.333	0 kept
16	p1q=0.005	AQFT_k1	4	violating	0.385	0.500	0.115	0 kept
16	p1q=0.010	QFT_full	2	srp	0.560	1.000	0.440	6 kept
16	p1q=0.010	QFT_full	2	violating	0.492	0.500	0.008	6 kept
16	p1q=0.010	QFT_full	4	srp	0.307	1.000	0.693	6 kept
16	p1q=0.010	QFT_full	4	violating	0.254	0.500	0.246	6 kept
16	p1q=0.010	AQFT_k1	2	srp	0.723	1.000	0.277	0 kept
16	p1q=0.010	AQFT_k1	2	violating	0.491	0.500	0.009	0 kept
16	p1q=0.010	AQFT_k1	4	srp	0.477	1.000	0.523	0 kept
16	p1q=0.010	AQFT_k1	4	violating	0.325	0.500	0.175	0 kept
16	p1q=0.020	QFT_full	2	srp	0.530	1.000	0.470	6 kept
16	p1q=0.020	QFT_full	2	violating	0.494	0.500	0.006	6 kept
16	p1q=0.020	QFT_full	4	srp	0.300	1.000	0.700	6 kept
16	p1q=0.020	QFT_full	4	violating	0.260	0.500	0.240	6 kept
16	p1q=0.020	AQFT_k1	2	srp	0.570	1.000	0.430	0 kept
16	p1q=0.020	AQFT_k1	2	violating	0.499	0.500	0.001	0 kept
16	p1q=0.020	AQFT_k1	4	srp	0.327	1.000	0.673	0 kept
16	p1q=0.020	AQFT_k1	4	violating	0.267	0.500	0.233	0 kept
32	ideal	QFT_full	2	srp	1.000	1.000	0.000	10 kept
32	ideal	QFT_full	2	violating	0.500	0.500	0.000	10 kept
32	ideal	QFT_full	4	srp	1.000	1.000	0.000	10 kept
32	ideal	QFT_full	4	violating	0.487	0.500	0.013	10 kept
32	ideal	AQFT_k1	2	srp	1.000	1.000	0.000	0 kept
32	ideal	AQFT_k1	2	violating	0.497	0.500	0.003	0 kept
32	ideal	AQFT_k1	4	srp	1.000	1.000	0.000	0 kept
32	ideal	AQFT_k1	4	violating	0.497	0.500	0.003	0 kept
32	p1q=0.005	QFT_full	2	srp	0.655	1.000	0.345	10 kept
32	p1q=0.005	QFT_full	2	violating	0.502	0.500	0.002	10 kept
32	p1q=0.005	QFT_full	4	srp	0.405	1.000	0.595	10 kept
32	p1q=0.005	QFT_full	4	violating	0.305	0.500	0.195	10 kept
32	p1q=0.005	AQFT_k1	2	srp	0.840	1.000	0.160	0 kept
32	p1q=0.005	AQFT_k1	2	violating	0.471	0.500	0.029	0 kept
32	p1q=0.005	AQFT_k1	4	srp	0.665	1.000	0.335	0 kept
32	p1q=0.005	AQFT_k1	4	violating	0.390	0.500	0.110	0 kept
32	p1q=0.010	QFT_full	2	srp	0.580	1.000	0.420	10 kept
32	p1q=0.010	QFT_full	2	violating	0.502	0.500	0.002	10 kept
32	p1q=0.010	QFT_full	4	srp	0.314	1.000	0.686	10 kept
32	p1q=0.010	QFT_full	4	violating	0.292	0.500	0.208	10 kept
32	p1q=0.010	AQFT_k1	2	srp	0.735	1.000	0.265	0 kept
32	p1q=0.010	AQFT_k1	2	violating	0.497	0.500	0.003	0 kept
32	p1q=0.010	AQFT_k1	4	srp	0.525	1.000	0.475	0 kept
32	p1q=0.010	AQFT_k1	4	violating	0.353	0.500	0.147	0 kept
32	p1q=0.020	QFT_full	2	srp	0.530	1.000	0.470	10 kept
32	p1q=0.020	QFT_full	2	violating	0.492	0.500	0.007	10 kept
32	p1q=0.020	QFT_full	4	srp	0.292	1.000	0.708	10 kept
32	p1q=0.020	QFT_full	4	violating	0.269	0.500	0.231	10 kept
32	p1q=0.020	AQFT_k1	2	srp	0.555	1.000	0.445	0 kept
32	p1q=0.020	AQFT_k1	2	violating	0.502	0.500	0.002	0 kept
32	p1q=0.020	AQFT_k1	4	srp	0.315	1.000	0.685	0 kept
32	p1q=0.020	AQFT_k1	4	violating	0.278	0.500	0.223	0 kept
64	ideal	QFT_full	2	srp	1.000	1.000	0.000	15 kept
64	ideal	QFT_full	2	violating	0.469	0.500	0.031	15 kept
64	ideal	QFT_full	4	srp	1.000	1.000	0.000	15 kept
64	ideal	QFT_full	4	violating	0.498	0.500	0.002	15 kept
64	ideal	AQFT_k1	2	srp	1.000	1.000	0.000	0 kept
64	ideal	AQFT_k1	2	violating	0.468	0.500	0.032	0 kept
64	ideal	AQFT_k1	4	srp	1.000	1.000	0.000	0 kept
64	ideal	AQFT_k1	4	violating	0.494	0.500	0.006	0 kept
64	p1q=0.005	QFT_full	2	srp	0.593	1.000	0.407	15 kept
64	p1q=0.005	QFT_full	2	violating	0.508	0.500	0.008	15 kept
64	p1q=0.005	QFT_full	4	srp	0.366	1.000	0.634	15 kept
64	p1q=0.005	QFT_full	4	violating	0.304	0.500	0.196	15 kept
64	p1q=0.005	AQFT_k1	2	srp	0.807	1.000	0.193	0 kept
64	p1q=0.005	AQFT_k1	2	violating	0.509	0.500	0.009	0 kept
64	p1q=0.005	AQFT_k1	4	srp	0.660	1.000	0.340	0 kept
64	p1q=0.005	AQFT_k1	4	violating	0.378	0.500	0.122	0 kept
64	p1q=0.010	QFT_full	2	srp	0.480	1.000	0.520	15 kept
64	p1q=0.010	QFT_full	2	violating	0.529	0.500	0.029	15 kept
64	p1q=0.010	QFT_full	4	srp	0.196	1.000	0.804	15 kept
64	p1q=0.010	QFT_full	4	violating	0.228	0.500	0.272	15 kept
64	p1q=0.010	AQFT_k1	2	srp	0.627	1.000	0.373	0 kept
64	p1q=0.010	AQFT_k1	2	violating	0.510	0.500	0.010	0 kept
64	p1q=0.010	AQFT_k1	4	srp	0.413	1.000	0.587	0 kept
64	p1q=0.010	AQFT_k1	4	violating	0.311	0.500	0.189	0 kept
64	p1q=0.020	QFT_full	2	srp	0.507	1.000	0.493	15 kept
64	p1q=0.020	QFT_full	2	violating	0.489	0.500	0.011	15 kept
64	p1q=0.020	QFT_full	4	srp	0.260	1.000	0.740	15 kept
64	p1q=0.020	QFT_full	4	violating	0.241	0.500	0.259	15 kept
64	p1q=0.020	AQFT_k1	2	srp	0.553	1.000	0.447	0 kept
64	p1q=0.020	AQFT_k1	2	violating	0.491	0.500	0.009	0 kept
64	p1q=0.020	AQFT_k1	4	srp	0.340	1.000	0.660	0 kept
64	p1q=0.020	AQFT_k1	4	violating	0.273	0.500	0.227	0 kept

Selene depolarizing-noise sweep on G1's coset predictor, now scaled across N ∈ {16, 32, 64}. QFT_full keeps every cphase in the QFT ladder (6 gates at N=16, 10 at N=32, 15 at N=64); AQFT_k1 is the rewriter-stripped variant (every cphase pruned). Under ideal shots AQFT_k1 is a known falsifier (over-pruned). Under depolarizing noise the missing 2-qubit gates avoid decoherence and AQFT_k1 catches up — the gap widens monotonically with N (+0.073 → +0.083 → +0.101 mean advantage at N=16/32/64) because QFT_full pays for O(n²) more cphase gates while AQFT_k1 stays linear in n. PASS = AQFT_k1 not-worse-than QFT_full in >=50% of noisy cells per N.