Native Asymmetric-Phase Gates Produce Sub-Poissonian Syndrome Statistics on Superconducting Quantum Processors: Cross-Architecture IBM Evidence and a Pre-Registered Willow Test
Syndrome extraction in superconducting quantum error correction often reports super-Poissonian count statistics on both hexagonal (IBM heavy-hex) and grid (Google Willow) architectures. A recent analysis of 756 IBM Eagle r3 experiments found the opposite: sub-Poissonian anti-bunching with Fano factor F = 0.856, distance-independent and with linear rather than super-linear burst scaling. We show that this signal is a property of a specific two-qubit operation — the P gate, defined as P(φ) = R_z(+φ) ⊗ R_z(−φ) — and not of the hardware on which it runs. On IBM Eagle r3 and Heron r2 the P gate compiles to two virtual-Z frame changes at transpiled depth 6 (zero duration, zero gate error); on Google Willow it compiles to a single PhXZ gate per qubit at transpiled depth 2, independent of the number of Floquet steps. On a 9-qubit triangle cell on ibm_strasbourg, paired circuits containing the P gate at matched transpiled depth (279) and two-qubit gate count (108 CX/ECR) return Fano F = 0.506 versus F = 0.564 for the unpaired control — a directional signature that cannot be attributed to decoherence because the two circuits differ only in the presence of the P gate. The aggregate Fano gap is ΔF = −0.058 ± 0.017 with 95% CI [−0.098, −0.031] (parametric bootstrap synthesising shot-level data from recorded edge fire rates, since raw shot counts are not preserved in the IBM Runtime JSON; B = 10 000; z = 3.4, p ≈ 6 × 10⁻⁴). The per-round Fano is the protocol observable (F_round ∈ [0.49, 0.65] across four sessions, paired and control alike); the aggregate gap is inflated by session-dependent round-to-round correlation (full forensics in the paper). Cross-architecture replication on ibm_kingston (Heron r2, different coupling map) reproduces the paired/control DTC 2T-subharmonic ratio at 3.43–3.92×, matching or exceeding the Eagle r3 range of 3.20–3.58×. A matched-protocol Monte Carlo of the same Floquet cycle on hexagonal and square grids shows that at τ ≥ 5 the square grid produces sub-Poissonian Fano factors as tight as F = 0.370 ± 0.026 (mean ± std across 30 PRNG seeds, 20 000 shots each) on a 4×4 cell — tighter than any hexagonal cell tested up to a 19-node r = 2 Eisenstein lattice. We pre-register eight falsifiable observables for a paired-phase Google Willow run (~1 QPU-hour, ~200 Cirq circuits at depth 2), with a timestamped PREDICTION.md committed to a public repository across three SHAs — 5bbfdb6f (2026-04-12), 745f653f (2026-04-15), and 30984cab (2026-04-19) — all before any Google hardware access. The eight predictions are quantitative and falsifiable; a Willow run inside the predicted ranges confirms platform-independence of the P-gate signature, while a result outside any threshold falsifies the corresponding component of the central claim. The sub-Poissonian signature is gate-dependent, and topology-agnostic in the deep-Floquet regime of the supporting Monte Carlo; hardware execution on Willow is the outstanding test. Scripts and data: https://doi.org/10.5281/zenodo.19663025. This paper consolidates and extends results from Papers 24, 25, and 26 of the Merkabit Research Series.
Syndrome extraction in superconducting quantum error correction often reports super-Poissonian count statistics on both hexagonal (IBM heavy-hex) and grid (Google Willow) architectures. A recent analysis of 756 IBM Eagle r3 experiments found the opposite: sub-Poissonian anti-bunching with Fano factor F = 0.856, distance-independent and with linear rather than super-linear burst scaling. We show that this signal is a property of a specific two-qubit operation — the P gate, defined as P(φ) = R_z(+φ) ⊗ R_z(−φ) — and not of the hardware on which it runs. On IBM Eagle r3 and Heron r2 the P gate compiles to two virtual-Z frame changes at transpiled depth 6 (zero duration, zero gate error); on Google Willow it compiles to a single PhXZ gate per qubit at transpiled depth 2, independent of the number of Floquet steps. On a 9-qubit triangle cell on ibm_strasbourg, paired circuits containing the P gate at matched transpiled depth (279) and two-qubit gate count (108 CX/ECR) return Fano F = 0.506 versus F = 0.564 for the unpaired control — a directional signature that cannot be attributed to decoherence because the two circuits differ only in the presence of the P gate. The aggregate Fano gap is ΔF = −0.058 ± 0.017 with 95% CI [−0.098, −0.031] (parametric bootstrap synthesising shot-level data from recorded edge fire rates, since raw shot counts are not preserved in the IBM Runtime JSON; B = 10 000; z = 3.4, p ≈ 6 × 10⁻⁴). The per-round Fano is the protocol observable (F_round ∈ [0.49, 0.65] across four sessions, paired and control alike); the aggregate gap is inflated by session-dependent round-to-round correlation (full forensics in the paper). Cross-architecture replication on ibm_kingston (Heron r2, different coupling map) reproduces the paired/control DTC 2T-subharmonic ratio at 3.43–3.92×, matching or exceeding the Eagle r3 range of 3.20–3.58×. A matched-protocol Monte Carlo of the same Floquet cycle on hexagonal and square grids shows that at τ ≥ 5 the square grid produces sub-Poissonian Fano factors as tight as F = 0.370 ± 0.026 (mean ± std across 30 PRNG seeds, 20 000 shots each) on a 4×4 cell — tighter than any hexagonal cell tested up to a 19-node r = 2 Eisenstein lattice. We pre-register eight falsifiable observables for a paired-phase Google Willow run (~1 QPU-hour, ~200 Cirq circuits at depth 2), with a timestamped PREDICTION.md committed to a public repository across three SHAs — 5bbfdb6f (2026-04-12), 745f653f (2026-04-15), and 30984cab (2026-04-19) — all before any Google hardware access. The eight predictions are quantitative and falsifiable; a Willow run inside the predicted ranges confirms platform-independence of the P-gate signature, while a result outside any threshold falsifies the corresponding component of the central claim. The sub-Poissonian signature is gate-dependent, and topology-agnostic in the deep-Floquet regime of the supporting Monte Carlo; hardware execution on Willow is the outstanding test. Scripts and data: https://doi.org/10.5281/zenodo.19663025. This paper consolidates and extends results from Papers 24, 25, and 26 of the Merkabit Research Series.
Syndrome extraction in superconducting quantum error correction often reports super-Poissonian count statistics on both hexagonal (IBM heavy-hex) and grid (Google Willow) architectures. A recent analysis of 756 IBM Eagle r3 experiments found the opposite: sub-Poissonian anti-bunching with Fano factor F = 0.856, distance-independent and with linear rather than super-linear burst scaling. We show that this signal is a property of a specific two-qubit operation — the P gate, defined as P(φ) = R_z(+φ) ⊗ R_z(−φ) — and not of the hardware on which it runs. On IBM Eagle r3 and Heron r2 the P gate compiles to two virtual-Z frame changes at transpiled depth 6 (zero duration, zero gate error); on Google Willow it compiles to a single PhXZ gate per qubit at transpiled depth 2, independent of the number of Floquet steps. On a 9-qubit triangle cell on ibm_strasbourg, paired circuits containing the P gate at matched transpiled depth (279) and two-qubit gate count (108 CX/ECR) return Fano F = 0.506 versus F = 0.564 for the unpaired control — a directional signature that cannot be attributed to decoherence because the two circuits differ only in the presence of the P gate. The aggregate Fano gap is ΔF = −0.058 ± 0.017 with 95% CI [−0.098, −0.031] (parametric bootstrap synthesising shot-level data from recorded edge fire rates, since raw shot counts are not preserved in the IBM Runtime JSON; B = 10 000; z = 3.4, p ≈ 6 × 10⁻⁴). The per-round Fano is the protocol observable (F_round ∈ [0.49, 0.65] across four sessions, paired and control alike); the aggregate gap is inflated by session-dependent round-to-round correlation (full forensics in the paper). Cross-architecture replication on ibm_kingston (Heron r2, different coupling map) reproduces the paired/control DTC 2T-subharmonic ratio at 3.43–3.92×, matching or exceeding the Eagle r3 range of 3.20–3.58×. A matched-protocol Monte Carlo of the same Floquet cycle on hexagonal and square grids shows that at τ ≥ 5 the square grid produces sub-Poissonian Fano factors as tight as F = 0.370 ± 0.026 (mean ± std across 30 PRNG seeds, 20 000 shots each) on a 4×4 cell — tighter than any hexagonal cell tested up to a 19-node r = 2 Eisenstein lattice. We pre-register eight falsifiable observables for a paired-phase Google Willow run (~1 QPU-hour, ~200 Cirq circuits at depth 2), with a timestamped PREDICTION.md committed to a public repository across three SHAs — 5bbfdb6f (2026-04-12), 745f653f (2026-04-15), and 30984cab (2026-04-19) — all before any Google hardware access. The eight predictions are quantitative and falsifiable; a Willow run inside the predicted ranges confirms platform-independence of the P-gate signature, while a result outside any threshold falsifies the corresponding component of the central claim. The sub-Poissonian signature is gate-dependent, and topology-agnostic in the deep-Floquet regime of the supporting Monte Carlo; hardware execution on Willow is the outstanding test. Scripts and data: https://doi.org/10.5281/zenodo.19663025. This paper consolidates and extends results from Papers 24, 25, and 26 of the Merkabit Research Series.
Syndrome extraction in superconducting quantum error correction typically produces super-Poissonian count statistics on both hexagonal (IBM heavy-hex) and grid (Google Willow) architectures. A recent analysis of 756 IBM Eagle r3 experiments found the opposite: sub-Poissonian anti-bunching with Fano factor F = 0.856, distance-independent and with linear rather than super-linear burst scaling. We show that this signal is a property of a specific two-qubit operation — the P gate, defined as P(φ) = R_z(+φ) ⊗ R_z(−φ) — and not of the hardware on which it runs. On IBM Eagle r3 and Heron r2 the P gate compiles to two virtual-Z frame changes at transpiled depth 6 (zero duration, zero gate error); on Google Willow it compiles to a single PhXZ gate per qubit at transpiled depth 2, independent of the number of Floquet steps. On a 9-qubit triangle cell on ibm_strasbourg, paired circuits containing the P gate at matched transpiled depth (279) and two-qubit gate count (108 CX/ECR) return Fano F = 0.506 versus F = 0.564 for the unpaired control — a directional signature that cannot be attributed to decoherence because the two circuits differ only in the presence of the P gate. The aggregate Fano gap of ΔF = −0.058 has a 95% CI of [−0.090, −0.025] (parametric bootstrap, B = 10 000; z = 3.4, p ≈ 6 × 10⁻⁴), excluding zero. The per-round signature is the protocol observable; the aggregate gap is inflated by session-dependent round-to-round correlation (full forensics in the paper). Cross-architecture replication on ibm_kingston (Heron r2, different coupling map) reproduces the paired/control DTC 2T-subharmonic ratio at 3.43–3.92×, matching or exceeding the Eagle r3 range of 3.20–3.58×. A matched-protocol Monte Carlo of the same Floquet cycle on hexagonal and square grids shows that at τ ≥ 5 the square grid produces sub-Poissonian Fano factors as tight as F = 0.370 ± 0.026 (mean ± std across 30 PRNG seeds, 20 000 shots each) on a 4×4 cell — tighter than any hexagonal cell tested up to a 19-node r = 2 Eisenstein lattice. We pre-register eight falsifiable observables for a paired-phase Google Willow run (~1 QPU-hour, ~200 Cirq circuits at depth 2), with a timestamped PREDICTION.md committed to a public repository (SHAs 5bbfdb6f on 2026-04-12 and 745f653f on 2026-04-15) before any Google hardware access. The eight predictions are quantitative and falsifiable; a Willow run inside the predicted ranges confirms platform-independence of the P-gate signature, while a result outside any threshold falsifies the corresponding component of the central claim. The sub-Poissonian signature is gate-dependent and topology-agnostic; hardware execution on Willow is the outstanding test. Scrips and data avilable: DOI: https://doi.org/10.5281/zenodo.19663025This is a combination paper created for submission and peer review based on Paper 24, 25 and 26.
Quantum error correction assumes that all syndrome activations represent errors requiring correction. We present evidence from 756 QEC runs across three IBM Eagle r3 processors that this assumption is wrong. The hardware exhibits sub-Poissonian syndrome statistics (Fano factor F = 0.856, t = -131 against Poisson, zero dependence on code distance), indicating that a fraction of syndrome events are not random noise but structured cooperative transitions. We introduce a regime classifier decoder that distinguishes binary errors (which should be corrected) from ternary transitions (which should not). On a mixed binary/ternary error model calibrated to IBM hardware statistics, the classifier reduces logical error rates by 7-19% at static detection depth (tau = 1) across all cell sizes, with statistical significance p < 0.05 in 7 of 8 test conditions (p < 0.0001 in all four tau = 1 conditions). The improvement mechanism is selective abstention: the classifier correctly identifies 75-98% of ternary transitions and leaves them uncorrected (75-81% at tau = 1, 88-98% at tau = 5), whereas a standard decoder miscorrects them, introducing errors that would not otherwise exist. A cross-platform control on Google's 105-qubit Willow processor (420 experiments, d = 3, 5, 7) shows the opposite: super-Poissonian statistics (F = 2.42), super-linear burst scaling, and positive spatial correlation -- confirming that the sub-Poissonian signal is absent from standard surface-code circuits that lack the P-gate asymmetry. The result demonstrates that standard QEC actively destroys quantum information by correcting valid ternary states, and that less correction produces better performance when the hardware has cooperative error structure.
The merkabit's sub-Poissonian error statistics are not a property of IBM's heavy-hex topology. They are a geometric effect that follows the P gate — two Z rotations with opposite signs — regardless of the hardware substrate. Three lines of evidence are presented. 1. Cross-architecture hardware validation. All five Appendix N predictions from the Base Paper are confirmed on IBM Eagle r3 (ibm_strasbourg, ibm_brussels) and IBM Heron r2 (ibm_kingston, 156 qubits, different coupling map). The full protocol was run on Strasbourg and Kingston; Brussels confirmed P5 independently. The P2 local minima at n = 13 (0.688 vs 0.709, ideal 0.696) and n = 27 (0.670 vs 0.694, ideal 0.683) show both architectures bracketing the ideal within 2%. The DTC paired/control ratio on Heron r2 (3.43–3.92×) matches or exceeds all Eagle r3 values (3.20–3.58×). P5 (DTC robustness) is confirmed in this paper's cross-architecture session, completing the Appendix N scorecard: five of five predictions retired on hardware within a single week (6–12 April 2026). 2. Corrected Willow interpretation. Paper 24's conclusion that the sub-Poissonian signal is "architecture-specific to heavy-hex" was premature. The Google Willow surface-code data (F = 2.42, super-Poissonian) lacked the P gate entirely; the comparison was paired-IBM vs unpaired-Google, not hex vs square. The signal is absent from circuits without the P-gate asymmetry, regardless of topology. 3. Square-grid topology simulation. A noisy Monte Carlo simulation comparing hexagonal and square grids under the pentachoric ouroboros cycle shows that at syndrome extraction depth τ ≥ 5, the square grid produces sub-Poissonian Fano factors — and at matched sizes, is more sub-Poissonian than hex at every error rate. The 4×4 square grid (16 nodes) achieves F = 0.285 at ε = 0.10, the tightest anti-bunching of any cell tested. Pre-registered prediction for Google Willow hardware (timestamped before any Google hardware access): Fano factor (2-qubit, τ = 5): F ≈ 0.3–0.7 DTC paired/control ratio: > 3× P1b sign flip: n = 6 → 8 P2 local minimum (n = 13): P ≈ 0.696 P2 quasi-period peak: n = 39 ± 2 Fano (4×4 square grid, τ = 5): F ≈ 0.29 Cirq implementations (P1b, P2, P5) compile to depth 2 on Google hardware via PhXZ gate merging. Total resource: ~200 circuits at 4,096 shots, less than one hour of QPU time. Appendix N scorecard (complete): P1 Berry phase — Confirmed (Paper 25) P2 Quasi-period — Confirmed (Paper 25) P3 Z₂ chirality symmetry — Confirmed (Paper 24) P4 Centre-node detection rate — Confirmed (Paper 24) P5 DTC robustness — Confirmed (this paper, 3 backends, 2 architectures) No error mitigation was applied to any hardware result. All results are from raw hardware counts. No prediction has been missed or revised after the fact. This is Paper 26 of the Merkabit research series.
Standard quantum error correction assumes that all syndrome activations represent errors requiring correction. This paper presents evidence from 756 QEC runs across three IBM Eagle r3 processors (ibm_brisbane, ibm_kyoto, ibm_osaka) that this assumption is incomplete. The hardware exhibits sub-Poissonian syndrome statistics — Fano factor F = 0.856 (t = −131 against Poisson) with zero dependence on code distance (ANOVA p = 0.79) and linear burst scaling (R² = 0.9999). These statistics indicate that a fraction of syndrome events are not random noise but structured cooperative transitions arising from the Z₃ chirality classes of IBM's heavy-hex (Eisenstein-compatible) lattice connectivity. A regime classifier decoder is introduced that distinguishes binary errors from ternary transitions using five structural features (isolation, boundary status, density contrast, chirality, temporal consistency). On a mixed error model calibrated to the IBM hardware statistics, the classifier reduces logical error rates by 7–19% at static detection depth (τ = 1) across all cell sizes, with p < 0.0001 in all four τ = 1 conditions. The improvement mechanism is selective abstention: the classifier correctly identifies 75–80% of ternary transitions at τ = 1 (88–98% at τ = 5) and leaves them uncorrected, whereas a standard decoder miscorrects them. A cross-platform control on Google's 105-qubit Willow processor (420 experiments, d = 3, 5, 7) shows the opposite statistics: super-Poissonian (F = 2.42), super-linear burst scaling, and positive spatial correlation. The Willow result is a prospective prediction of the Merkabit framework (Paper 15), which identifies hexagonal connectivity as the structural requirement for Z₃ chirality-driven anti-bunching. IBM's heavy-hex architecture satisfies this requirement; Google's grid architecture does not. The classifier applied to Willow produces zero improvement, confirming the effect is architecture-specific. The IBM sub-Poissonian statistics were consistent with Paper 15's framework when the DAQEC benchmark became available. The Willow analysis was conducted after Paper 15 was complete, on data not previously examined, and constitutes the prospective test. Direct hardware validation (§2.7): A hexagonal syndrome circuit (7-node cell, 12 CNOTs per round, T = 20 rounds, 4,000 shots) was run on real IBM Quantum hardware by Thor Henning Hetland. On ibm_strasbourg (Eagle r3) with native-direction CX gates, F = 0.9611 < 1 — sub-Poissonian, confirming the prediction on a processor and circuit independent of the original analysis. The routed circuit on the same processor gives F = 1.207, and ibm_fez (Heron r2) gives F = 18.75 — both super-Poissonian. The signal is gate-direction-sensitive: wrong-direction CX gates inflate circuit depth from 1163 to 2045, destroying the anti-bunching structure. This sensitivity confirms the effect is geometric: it depends on preserving native hexagonal connectivity at the gate level. Key results: F = 0.856 ± 0.03 (IBM) vs F = 2.42 ± 0.36 (Willow) · linear burst scaling R² = 0.9999 (IBM) · 7–19% LER improvement · zero classifier effect on Willow · f = 14.4% ternary fraction Data sources: IBM DAQEC benchmark, Zenodo 10.5281/zenodo.17881116 · Google Willow surface code data, Zenodo 10.5281/zenodo.13273331
We report the first experimental validation of the merkabit dual-spinor architecture across four circuit families on IBM ibm_strasbourg (Eagle r3, 127 qubits), executed 6–7 April 2026. The central discovery is that the merkabit's defining operation — the P gate, applying asymmetric phase to counter-rotating spinors — compiles to two native Rz gates with opposite signs: P(φ) = Rz(+φ) ⊗ Rz(−φ). On IBM Eagle r3, both Rz gates are virtual-Z frame changes requiring zero duration, zero error, and zero additional circuit depth. The P gate is native. Eight independent hardware results confirm the architecture, spanning 2 to 26 qubits: Ouroboros return fidelity ZP-ORF = 0.968, transpiler confirming U₀†U₀ = I at depth 1 π-lock standing wave ⟨ZZ⟩ = +0.44 vs +0.447 ideal (2% agreement, two independent runs) Parity witness ⟨XX⟩ = −0.450, consistent with |Φ⁻⟩-like entanglement at 90° Bloch separation Z₂ chirality symmetry mean error 0.016 across n = 4, 6, 8, 12 — all below readout noise threshold; non-monotonic ⟨ZZ⟩ breathing confirmed as standing-wave signature Two-scale Fano structure (9-qubit triangle): intra-round Fano F ≈ 0.52–0.54, within-τ dispersion σ ≤ 0.004 across 18 hardware rounds at τ ∈ {1, 5, 12} Inter-round coherence ρ ≈ 0.86 on the same triangle cell, confirming the two-scale standing-wave memory signature predicted by Paper 15 Full pentachoric error detection (26-qubit, 7-node Eisenstein cell): detection rate 0.089 (baseline) → 0.988 (injected), a 89.9 pp jump; 28/28 single-gate injections above 97% Centre-node syndrome weight 2× periphery matching Eisenstein lattice coordination; sub-Poissonian Fano on every injection (F_centre = 0.055 ± 0.009, F_periphery ≈ 0.20); Z₂ chirality symmetry confirmed inside the Fano structure Four of seven formal predictions from earlier papers in the series are retired by hardware data: P3 (Z₂ symmetry, mean error 0.016 vs <5% threshold), P4 (centre-node detection rate, 99.3% vs 91% ± 5% predicted, exceeding the upper tolerance by 3.3 pp), rotation-gap flatness, and two-scale Fano separation. Three predictions (P1 Berry phase, P2 quasi-period, P5 DTC robustness) remain pending for a subsequent session. A cross-platform reanalysis of Google Quantum AI's 420-experiment Willow dataset shows the opposite sign on every metric (F = 2.42 super-Poissonian, super-linear burst scaling, positive spatial correlation), consistent with a topology distinction: IBM heavy-hex maps naturally onto the Eisenstein lattice; Willow's square grid does not. No error mitigation, post-selection, or parameter tuning was applied to any primary result. Keywords: merkabit, dual spinor, P gate, quantum error correction, sub-Poissonian statistics, Eisenstein lattice, pentachoric code, IBM Eagle r3, Google Willow, standing wave, π-lock, Z₂ symmetry, Fano factor, Floquet time crystal