July 2026 · Pre-registered · Four points
Gyawali et al. motivate gauge-sector physics on Willow (arXiv:2410.06557). QPC runs a pre-registered architecture instance on the same ICC stack as the Joint Structure Challenge — not a Willow circuit re-run.
Plain English
What QPC delivers — forward framing
We claim: the superposition-versus-sampling occurrence that motivates disorder-free localization in lattice gauge theory is native to polycontextural architecture — even / odd / bridge gauge sectors mapped to three contextures in one IBM Fez job, with cross-boundary ICC on raw measurement counts (3/3 pass, gaps 0.349 · 0.243 · 0.131, public job IDs). Sector structure is topology, not a custom Hamiltonian program: the same logical fact Google’s team proved in physics on Willow, QPC makes executable and auditable on IBM Heron in one pre-registered protocol — in some hours of work.
Gyawali et al. (arXiv:2410.06557 · Science 2026) showed in fundamental physics that gauge-sector superposition ≠ incoherent disorder sampling. MCGS shows that distinction on commercial gate hardware: coupled polycontextural execution produces ICC that separable multi-job and intracontext controls cannot reproduce — coupling-borne, not depth-borne, no decoder, no mitigation stack.
Customer takeaway: QPC does not wait for a bespoke lattice-gauge circuit. It encodes sector splits as contextures + transjunctions and proves the architecture signature where buyers can verify it — IBM job IDs, raw counts, pre-registered bar.
| What QPC proves on IBM Fez | Honest scope (not this page) |
|---|---|
| Coherent multi-sector structure vs factorized execution (ICC witness) | Willow LGT circuit parity |
| One coupled job beats separable 3-job + intracontext controls (28× · 26× · 8×) | Error-mitigated gauge polarization time series |
| Sector topology as first-class QPC encoding — fast path to auditable hardware proof | Classical intractability or supremacy claims |
Scope note: Point 1 is ED sanity; Point 4 is analytic motivation. This is Lane A architecture evidence, not a replacement for Google’s full experimental physics program.
This page is Lane A (Topology Certificate). Industry pilots with customer scores live on Heron trilogy (Lane B).
Question: Does coupled polycontextural wiring show up in raw hardware?
Question: What business outcome does polycontextural execution deliver?
IBM Fez result (July 2026): Raw ICC gaps vs 3-job separable control 0.349 · 0.243 · 0.131 (seeds 7, 11, 42) · 3/3 pass. Against the intracontext control, the same coupled results separate 28× · 26× · 8× (coupled ICC ÷ intracontext ICC). Every coupled result clears 3× against both controls — the separation tracks cross-context coupling, not any single baseline.
The signal is coupling-borne, not depth-borne, and two controls bracket the depth confound from both sides: the intracontext control runs at its own depth (~127–131) and sits at floor; the separable multi-job control is itself deep yet also stays at floor. If circuit depth alone produced ICC, the deep separable control would show it regardless of wiring — it does not. Only cross-context transjunction coupling raises ICC above floor.
No mitigation. No decoder. No classical solver in the loop.
The separation you see is in the raw quantum measurement counts. Points 2 and 3 pass on unprocessed IBM Fez output — no readout mitigation, no problem-aware decoder, no post-selection. The inter-context correlation is carried by the polycontextural circuit topology itself and is auditable from the public job IDs. Most published near-term quantum optimization results reach their headline figure through a decoder or an error-mitigation stack; this result does not — scoped to ICC architecture witness only, not to QPC industry optimization pilots.
How we report (pre-registered): Primary pass/fail uses raw IBM counts. Same JSC bar: coupled ICC ≥ 0.02, gap ≥ 0.05, ratio ≥ 3× vs each control. Hardware arm = soft-objective QPC circuits with sector-motivated weights — not Trotterized LGT dynamics. Point 4 (Null B) is an analytic disorder-average argument; Points 2–3 are the IBM headline.
Two independent controls, two ratios. Each coupled result is tested against both a separable multi-job control (Point 2) and an intracontext control (Point 3). These are different baselines, so a given seed has two ratios — e.g. seed 11 separates 18× from the separable control and 26× from the intracontext control; seed 42 shows 10× vs separable and 8× vs intracontext (higher intracontext floor). A pass requires clearing 3× against both.
1D Z₂-inspired patch · gauge-sector superposition over 8 physical states · confinement ξ∞ = 1.29 < bar 2.5.
ED reference only — not the hardware headline. Persistence margin weak at L=5 (finite-size); confinement is the primary ED bar.
Three contextures with even / odd / bridge weight priors (motivated by gauge-sector split) · 4096 shots · couple_scale=0.8.
| Seed | Raw ICC gap | Separable ICC | Ratio vs separable control (≥3×) | Coupled job |
|---|---|---|---|---|
| 7 | 0.349 | 0.011 | 32× | d93up0fu62ks7395c3k0 |
| 11 | 0.243 | 0.014 | 18× | d93vk1dgc6cc73feg13g |
| 42 | 0.131 | 0.015 | 10× | d93vllvu62ks7395d7og |
Aer pre-check: 3/3 · mean gap 0.458 at couple_scale=0.8.
Pre-registered Aer coupling sweep (before Fez): couple_scale
0.8 → 0.458 · 1.0 → 0.441 · 1.2 → 0.357
(mean ICC gap vs separable, 3/3 pass at each point). IBM ran at sweep-selected best (0.8) — not tuned after hardware.
One job; coupling budget rewired within each context only (no cross-boundary transjunctions).
| Seed | Intracontext ICC | Ratio vs intracontext control (≥3×) | Intracontext job |
|---|---|---|---|
| 7 | 0.013 | 28× | d93up0vu62ks7395c3kg |
| 11 | 0.010 | 26× | d93vk1kql68s73c8tnm0 |
| 42 | 0.019 | 8× | d93vlmfu62ks7395d7pg |
Seed 42 shows the smallest margin (8×), driven by a higher intracontext floor (0.019 vs 0.010–0.013); it still clears the pre-registered 3× bar. Reported explicitly rather than absorbed into a range.
Not an IBM measurement. Analytic: sector probes a(s)=(-1)^s, b(s)=1 ⇒ Covs(a,b) = 0 — the connected term Γ in a coherent superposition is inaccessible to incoherent disorder sampling. This formalizes the motivation from Gyawali et al.; Points 2–3 test whether QPC’s ICC signature clears on hardware.
| Point | Metric | IBM Fez | Status |
|---|---|---|---|
| 1 | ED confinement ξ∞ | 1.29 < 2.5 | Pass (ED) |
| 2 | Raw ICC gap vs separable | 0.349 · 0.243 · 0.131 | Pass 3/3 |
| 3 | Raw ICC vs intracontext | 28× · 26× · 8× | Pass 3/3 |
| 4 | Null B Covs=0 | Analytic (ED note) | Pass (theory) |
Overall (pre-registered): IBM Points 2–3 3/3 pass raw · Point 1 ED confinement pass · Point 4 analytic pass · bundle results/qpc_mcgs_bundle.json
Pre-registration: docs/QPC_MCGS_PREREGISTRATION.md · MCQST outreach draft: docs/QPC_MCGS_MCQST_OUTREACH.md
.venv/bin/python3 vendor_benchmarks/qpc_mcgs/mcgs_icc_runner.py --mode ed .venv/bin/python3 vendor_benchmarks/qpc_mcgs/mcgs_icc_runner.py --mode aer-sweep .venv/bin/python3 vendor_benchmarks/qpc_mcgs/mcgs_icc_runner.py --mode ibm --backend ibm_fez --seeds 7,11,42 .venv/bin/python3 vendor_benchmarks/qpc_mcgs/mcgs_bundle.pyJoint Structure Challenge → ICC methodology → Machine bundle JSON → IBM Fez results JSON → Scripts README →