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.
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.
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
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.
Quantum error correction can suppress logical errors exponentially with code distance when physical noise is below threshold. Realizing this on hardware requires tight coordination among quantum gates, mid-circuit measurements, and qubit coherence. Device variation, noise asymmetry, and correlations across space and time complicate the translation of these capabilities into logical error suppression. Here, we study rotated surface-code memory on an IBM Nighthawk r2 processor. Performance varies across tested processor placements, which we attribute to differences in qubit quality. We optimize the code by combining short readout, fused measurement and reset, and an XX echo on data qubits during ancilla readout. Compared with standard readout without reset or echo, the optimized syndrome extraction circuit reduces the median per-round logical error rate by factors of 3.8 in the X basis and 1.4 in the Z basis. In memory experiments of up to 150 rounds, the distance advantage weakens, alongside long-lived correlations that may reflect a persistent error component. Under our optimization recipe, increasing the protected distance from 3 to 6 while holding the other distance fixed reduces the per-round logical error rate from 0.53% to 0.24% in Z memory and from 0.52% to 0.22% in X memory. The corresponding error-suppression factors under maximum-likelihood decoding are 1.68 and 1.85. These results connect circuit compilation and optimization to surface-code memory performance and limitations, and motivate QPU and QEC circuit codesign for fault-tolerant quantum computing primitives on current cloud hardware.
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.
Decoders for quantum error correction (QEC) experiments rely on detector error models (DEMs), which encode, for each error, its probability and the detectors and logical observables it flips. Here we show that estimating DEM event probabilities from experimental syndromes is feasible, avoids independent device benchmarking, and produces useful decoder priors for estimating and reducing decoded logical error probabilities. We evaluate our methods using open-source data from surface-code memory experiments performed on Google's Willow chip, and we carry out analogous surface-code experiments on IBM's \texttt{ibm\_miami} processor. Despite the different physical error scales of the Google and IBM devices, in both cases our estimated DEMs improve logical error probabilities relative to baseline device-informed DEMs, typically at the 5%−10% level and with larger gains in some IBM cases, without additional calibration circuits, decoder fine-tuning, or supervised fitting to logical outcomes.
Quantum error-correcting decoders provide both corrections and confidence estimates for the logical-error risk of individual measurement records. Such confidence can guide postselection, but it depends on the accuracy of the decoder noise model. When the physical device drifts away from that model, confidence measures such as the logical gap can become miscalibrated. We show that this mismatch can itself provide useful information. On IBM quantum hardware, syndrome statistics drift across consecutive acquisition windows, and the resulting detector histories differ substantially from those predicted by the stationary detector error model used for decoding. We observe a similar hardware-model mismatch in independent Google surface-code memory data. We exploit this effect by assigning additional rejection weight to detector histories that are unlikely under the assumed model. For minimum-weight perfect matching (MWPM), the minimum weight W provides an inexpensive proxy for syndrome surprisal. On held-out IBM repetition-code memories, likelihood-aware postselection reduces the retained logical-error probability (LEP) by 10.6% at d=7 and 28.8% at d=9, both at 15% rejection. On Google ten-round d=5 XZZX surface-code memory data, it reduces retained LEP by 75.4% at 90% rejection. Applied to Google's magic-state cultivation experiment with the Tesseract decoder, it reduces tomography infidelity by 34.7% with 30% additional grafting-stage rejection, or increases accepted yield by 30.4% at a target fidelity of 97.0%. Burst-noise simulations show that the advantage persists as code distance and syndrome-extraction volume increase. The method reuses quantities already produced during logical-gap decoding and requires only an additional fitting step.