Recognition: unknown
The Rotation Gap Is Not An Error: Ternary Structure in IBM Quantum Hardware
Pith reviewed 2026-05-10 15:37 UTC · model grok-4.3
The pith
IBM quantum hardware produces structured ternary transitions that standard QEC wrongly corrects, increasing logical errors.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The hardware exhibits sub-Poissonian syndrome statistics (F = 0.856) indicating that a fraction of syndrome events are structured cooperative transitions rather than random noise. A regime classifier decoder distinguishes binary errors requiring correction from ternary transitions that should be left uncorrected, achieving 7-19 percent lower logical error rates by correct abstention on 75-98 percent of the latter.
What carries the argument
The regime classifier decoder, which identifies ternary transitions from syndrome patterns and selectively abstains from correction on them.
If this is right
- On mixed binary/ternary error models the classifier reduces logical error rates by 7-19 percent at static detection depth across all cell sizes.
- The classifier correctly identifies 75-98 percent of ternary transitions and leaves them uncorrected, while standard decoders miscorrect them.
- Sub-Poissonian statistics show zero dependence on code distance, consistent with cooperative transitions rather than independent noise.
- A cross-platform control on Google's Willow processor yields super-Poissonian statistics and positive spatial correlation, confirming the effect is tied to IBM circuit asymmetry.
Where Pith is reading between the lines
- QEC decoders may need to be calibrated to each hardware platform's specific error correlations rather than using universal correction rules.
- Circuit designs that minimize P-gate asymmetry could reduce the occurrence of ternary transitions and simplify decoding.
- Similar statistical tests on other quantum processors might reveal additional non-binary error regimes that benefit from abstention-based decoding.
Load-bearing premise
The sub-Poissonian syndrome statistics arise from ternary transitions inherent to the hardware rather than from measurement effects or other correlations.
What would settle it
Measuring the Fano factor on IBM hardware using surface-code circuits that lack the P-gate asymmetry, or repeating the runs on an IBM device without that gate asymmetry, to test whether the Fano factor remains below one.
Figures
read the original abstract
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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript claims that quantum error correction incorrectly assumes all syndrome activations are errors requiring correction. Evidence from 756 QEC runs on three IBM Eagle r3 processors shows sub-Poissonian syndrome statistics (Fano factor F=0.856, t=-131 vs. Poisson, independent of code distance), interpreted as indicating structured ternary transitions. A regime classifier decoder is proposed to distinguish binary errors (correct) from ternary transitions (abstain), yielding 7-19% logical error rate reduction on a calibrated mixed error model at tau=1 (p<0.05 in most conditions). A Google Willow control (420 runs) exhibits super-Poissonian statistics (F=2.42), supporting hardware specificity due to P-gate asymmetry.
Significance. If the central interpretation holds, the work has notable significance for QEC by demonstrating that standard decoders can introduce errors through over-correction of valid states in hardware with cooperative transitions, potentially enabling abstention-based improvements. The scale of experiments, statistical rigor (Fano factor, t-test, distance independence), and cross-platform contrast are strengths. However, the result's impact depends on confirming the ternary mechanism over alternatives, which would affect decoder design for IBM-like systems.
major comments (2)
- [Abstract] Abstract: The headline interpretation that F=0.856 directly evidences 'structured cooperative transitions' that are ternary and should be left uncorrected is not uniquely supported by the data. Sub-Poissonian statistics are compatible with alternative mechanisms (negative temporal correlations in binary errors, measurement leakage, or finite-shot bias) that do not require a distinct ternary regime or abstention strategy; no distinguishing test (e.g., pulse tomography on the identified subset) is described.
- [Decoder evaluation] Decoder evaluation (results on mixed model): The 7-19% improvement at tau=1 is assessed exclusively on a mixed binary/ternary error model whose parameters are calibrated to the same IBM syndrome statistics used to detect the sub-Poissonian signal. This creates circularity in the performance claim, as the classifier is trained and evaluated on synthetic data derived from the observations it seeks to explain; the Google control uses dissimilar circuits and does not isolate the claimed P-gate cause.
minor comments (2)
- [Abstract] The abstract reports classifier accuracy (75-98% identification of ternary events) but provides no details on the classifier architecture, input features, or training procedure, hindering assessment of its generality.
- [Methods] No mention of raw data availability, exact syndrome extraction circuit parameters, or full experimental protocol (e.g., how the 756 runs were distributed across processors and distances), which would be needed for independent reproduction.
Simulated Author's Rebuttal
We thank the referee for their constructive and detailed comments. We address each major point below, providing clarifications on the interpretation of our results and indicating revisions to improve the manuscript.
read point-by-point responses
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Referee: The headline interpretation that F=0.856 directly evidences 'structured cooperative transitions' that are ternary and should be left uncorrected is not uniquely supported by the data. Sub-Poissonian statistics are compatible with alternative mechanisms (negative temporal correlations in binary errors, measurement leakage, or finite-shot bias) that do not require a distinct ternary regime or abstention strategy; no distinguishing test (e.g., pulse tomography on the identified subset) is described.
Authors: We acknowledge that sub-Poissonian Fano factors are not uniquely diagnostic of ternary transitions and could arise from negative temporal correlations among binary errors, leakage, or finite-shot effects. However, the observed F=0.856 is independent of code distance across d=3,5,7, which is inconsistent with leakage or depth-dependent biases that would typically strengthen with larger circuits. The Google Willow control (standard surface-code circuits, F=2.42, super-linear burst scaling) provides a hardware-specific contrast supporting that the sub-Poissonian signal is tied to IBM's P-gate asymmetry rather than a generic statistical artifact. While we have not performed pulse tomography on the low-syndrome subset, the regime classifier's selective abstention yields consistent 7-19% logical-error reduction under the calibrated model, demonstrating practical value even if the microscopic mechanism requires further confirmation. We will revise the abstract and add a dedicated limitations paragraph discussing alternative mechanisms and the value of future tomography experiments. revision: partial
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Referee: The 7-19% improvement at tau=1 is assessed exclusively on a mixed binary/ternary error model whose parameters are calibrated to the same IBM syndrome statistics used to detect the sub-Poissonian signal. This creates circularity in the performance claim, as the classifier is trained and evaluated on synthetic data derived from the observations it seeks to explain; the Google control uses dissimilar circuits and does not isolate the claimed P-gate cause.
Authors: The mixed model parameters are fitted directly to the empirical IBM syndrome counts to embed a ternary component whose statistics reproduce the observed sub-Poissonian behavior. The reported improvement is not circular because it quantifies the benefit of abstention versus mandatory correction under that hypothesis; if the sub-Poissonian signal were produced solely by binary correlations without a distinct regime, the classifier would not improve performance. The Google Willow experiments, although using standard surface-code circuits, serve as a negative control showing the opposite (super-Poissonian) statistics precisely when the P-gate asymmetry is absent, thereby isolating the effect to IBM hardware rather than circuit topology. We will expand the methods and results sections to explicitly describe the calibration procedure, include sensitivity checks on model parameters, and clarify the role of the cross-platform control. revision: partial
Circularity Check
Logical-error improvement demonstrated only on synthetic model calibrated to the same hardware statistics used for the Fano-factor claim
specific steps
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fitted input called prediction
[Abstract (performance paragraph)]
"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 error model is explicitly calibrated to the IBM hardware statistics that include the observed sub-Poissonian Fano factor. The 7-19% reduction is therefore computed inside a synthetic ensemble whose statistics were fitted to match the input data; the 'improvement' is a within-calibration comparison rather than an out-of-sample prediction.
full rationale
The paper measures a genuine sub-Poissonian Fano factor (F=0.856) from 756 real IBM runs; that datum is external. However, the headline performance result (7-19% reduction) is obtained by training and evaluating the regime classifier exclusively on a mixed binary/ternary error model whose parameters were calibrated to reproduce those same IBM statistics. Consequently the reported gain is a within-model comparison rather than an independent prediction or hardware verification. The Google Willow control supplies an external contrast but does not test the classifier on real IBM data. This produces partial circularity of the 'fitted input called prediction' type without rendering the entire derivation self-referential.
Axiom & Free-Parameter Ledger
free parameters (1)
- mixed binary/ternary error model calibration parameters
axioms (1)
- domain assumption Syndrome statistics can be used to classify events into binary errors requiring correction and ternary transitions that should be left alone
invented entities (1)
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ternary transitions
no independent evidence
Reference graph
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Miscorrecting a ternary transition (unique to the paradigm) The regime classifier eliminates the second failure mode by identifying ternary transitions and leaving them alone. FIG. 5. The miscorrection mechanism. Standard decoders (top, red) treat all syndrome activations as errors and correct every flagged node. When 14.4% of activations are ternary tran...
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A regime classifier decoder that reduces logical error rates by 7–19% through selective abstention—correctly identifying ternary transitions 75–98% of the time and leaving them uncorrected (75–81% atτ= 1, 88–98% atτ= 5). The result demonstrates a principle that inverts the standard logic of quantum error correction: when the hardware has cooperative struc...
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Evidence from This Paper’s Data The Fano factors measured in Section II B at code distanced= 7 (matching the cell size) are: •ibm brisbane:F(d=7) = 0.8303,F/7 = 0.1186 (deviation from 5/42: 0.4%) •ibm kyoto:F(d=7) = 0.8584,F/7 = 0.1226 (deviation from 5/42: 3.0%) 24 •ibm osaka:F(d=7) = 0.8360,F/7 = 0.1194 (deviation from 5/42: 0.3%) The mean atd= 7 isF= 0...
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