arxiv: 2604.14296 · v1 · submitted 2026-04-15 · 🪐 quant-ph

Recognition: unknown

Scalable quantum error correction tailored for a heavy-hex qubit array

Seok-Hyung Lee , Xanda C. Kolesnikow , Jun Zen , Evan T. Hockings , Campbell K. McLauchlan , Georgia M. Nixon , Thomas R. Scruby , Stephen D. Bartlett

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Robin Harper Benjamin J. Brown

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:10 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum error correctionheavy-hex latticedynamic compass codesubsystem codenoise-informed decodingsuperconducting qubitslogical error ratesyndrome extraction

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The pith

A dynamic compass code on heavy-hex hardware cuts logical errors by up to 38.3 percent with noise-informed decoding.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the dynamic compass code, a subsystem code whose syndrome extraction cycle is designed to use qubits efficiently on a heavy-hex lattice. The authors implement a distance-5 version on superconducting hardware and feed the decoder with detailed context-dependent error rates measured across the full extraction cycle plus soft information that flags measurement errors and leakage events. This noise-informed strategy produces up to 38.3 percent lower logical error rates than standard decoding on the same device. The work matters because it shows how matching both the code layout and the decoder to the actual noise of existing hardware can reduce the resources needed for reliable quantum computation. If the approach holds, error correction becomes more practical on near-term devices without requiring perfectly uniform or low-noise qubits.

Core claim

The dynamic compass code is a subsystem code with a novel syndrome extraction cycle that fits the heavy-hex lattice. Implementing a distance-5 instance on a superconducting qubit array and using averaged circuit eigenvalue sampling to obtain context-dependent error rates for every element of the syndrome extraction, together with soft measurement information to detect and post-select out leakage errors, yields up to 38.3 percent improvement in the logical error rate.

What carries the argument

The dynamic compass code, a subsystem code with a novel syndrome extraction cycle for heavy-hex lattices, paired with a decoder that uses context-dependent error rates and soft measurement data.

Load-bearing premise

The error rates obtained from averaged circuit eigenvalue sampling must accurately represent the full syndrome extraction cycle, and post-selection to remove leakage events must not introduce unacceptable bias into the logical error rate figures.

What would settle it

Re-running the identical distance-5 experiment with a standard decoder that assumes uniform error rates and finding that the logical error rate is no higher than the noise-informed result.

Figures

Figures reproduced from arXiv: 2604.14296 by Benjamin J. Brown, Campbell K. McLauchlan, Evan T. Hockings, Georgia M. Nixon, Jun Zen, Robin Harper, Seok-Hyung Lee, Stephen D. Bartlett, Thomas R. Scruby, Xanda C. Kolesnikow.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 7.** Figure 7: summarises the comparison. In each variant, the probability three-tuple p = (p0, p1, p2) yielded by the GMM (see Methods Secs. IV A and IV B) is used to update measurement-related error rates in the DEM on a shot-byshot basis, while all non-measurement noise parameters are kept fixed to the values obtained from the offline ACES characterisation. The variants differ only in the precise update rule and in t… view at source ↗

read the original abstract

To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that accommodate device-specific noise characteristics. Here, we introduce the \emph{dynamic compass code}, a subsystem code with a novel syndrome extraction cycle, that has a competitive threshold while making efficient use of qubits arranged on a heavy-hex lattice. We use a superconducting qubit array to implement a distance-5 instance of this code, and demonstrate how detailed noise characterisation can boost decoder performance to yield significant improvements in logical error rates. We perform averaged circuit eigenvalue sampling (ACES) to acquire detailed context-dependent error information on all elements of the syndrome extraction process. Furthermore, we leverage soft information produced from measurement devices to augment the decoder with measurement error information and detect leakage errors for exclusion through post-selection. Our noise-informed approach yields up to 38.3\% improvement in the logical error rate of a distance-5 implementation of the dynamic compass code in experiment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a new dynamic compass code for heavy-hex arrays plus a distance-5 experiment that uses ACES noise data and leakage post-selection to cut logical errors by 38%, but the post-selection step is not yet shown to be bias-free.

read the letter

The main takeaway is that this work puts a subsystem code on real superconducting hardware and gets measurable gains by feeding device-specific noise into the decoder. The dynamic compass code and its syndrome cycle are new enough to stand out from prior compass and heavy-hex constructions, and the ACES sampling plus soft-information decoding is a practical step forward from generic models. Running distance-5 and reporting a concrete improvement is better than most code papers that stop at thresholds or simulations. That part earns credit for moving the idea into experiment. The post-selection on leakage events is the clearest soft spot. The 38.3% figure is measured after dropping those shots, yet the abstract gives no acceptance fraction, no filtered-versus-unfiltered comparison, and no check that ACES matches the observed syndromes on the device. If leakage correlates with logical failures or if many shots are discarded, the reported gain becomes a conditional number rather than an operational one. The lack of error bars or baseline details in the summary also makes the claim harder to weigh without the full methods. This paper is for groups already working on superconducting error correction and hardware-aware decoders. Readers who need concrete examples of noise-informed decoding will get usable methods and data. It has enough experimental grounding to deserve a serious referee, though the review should ask for the missing post-selection statistics and ACES validation. I would send it to peer review with those requests.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces the dynamic compass code, a subsystem code with a novel syndrome extraction cycle tailored to heavy-hex lattices. It reports an experimental distance-5 implementation on a superconducting qubit array, using averaged circuit eigenvalue sampling (ACES) to obtain context-dependent error rates for the full syndrome cycle, combined with soft-information leakage detection and post-selection to augment a noise-informed decoder. The central claim is that this approach yields up to 38.3% improvement in logical error rate relative to standard decoding.

Significance. If the experimental results are robust, the work demonstrates that device-specific noise modeling via ACES and leakage-aware post-selection can deliver substantial gains in logical performance for distance-5 codes on real superconducting hardware. This is a meaningful step toward scalable, hardware-tailored QEC, particularly for heavy-hex architectures, and highlights the value of detailed context-dependent error characterization over generic decoders.

major comments (3)

[Abstract] Abstract: the reported 38.3% logical error rate improvement is presented without error bars, acceptance fractions for the post-selection step, or direct comparison of filtered versus unfiltered logical error rates, leaving open whether the gain reflects operational performance or a conditional metric after leakage exclusion.
[Experimental results (distance-5 implementation section)] Experimental results (distance-5 implementation section): the assumption that ACES accurately captures joint error statistics across the full syndrome extraction cycle (including gate-measurement-reset correlations) is central to the noise-informed decoder, yet no cross-validation against observed syndrome statistics or syndrome histogram comparisons is described to confirm predictive accuracy.
[Decoder and post-selection description] Decoder and post-selection description: without quantified acceptance rates or a side-by-side logical error rate comparison on the same dataset with and without leakage post-selection, it is unclear whether the 38.3% figure is load-bearing or could be materially altered by the filtering bias.

minor comments (2)

Clarify the precise definition of the dynamic compass code's syndrome extraction cycle relative to standard compass or surface-code cycles, including any additional reset or measurement operations.
Ensure all experimental figures report the number of shots, circuit repetitions, and any statistical uncertainties on the logical error rates.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments, which have helped us improve the clarity of our presentation regarding the experimental results and the validation of our noise-informed decoding approach. We address each major comment below and have revised the manuscript accordingly to provide the requested details and comparisons.

read point-by-point responses

Referee: [Abstract] Abstract: the reported 38.3% logical error rate improvement is presented without error bars, acceptance fractions for the post-selection step, or direct comparison of filtered versus unfiltered logical error rates, leaving open whether the gain reflects operational performance or a conditional metric after leakage exclusion.

Authors: We agree that the abstract would benefit from greater transparency on these points. The 38.3% figure is the improvement delivered by the complete noise-informed decoder, which incorporates both ACES-derived error rates and leakage post-selection via soft information. In the revised manuscript we have added error bars to the reported improvement, stated the post-selection acceptance fraction, and included a direct side-by-side comparison of logical error rates on the same dataset with and without the leakage-exclusion step. This shows that the gain arises from the combined effect of context-dependent noise modeling and soft-information augmentation rather than filtering alone. revision: yes
Referee: [Experimental results (distance-5 implementation section)] Experimental results (distance-5 implementation section): the assumption that ACES accurately captures joint error statistics across the full syndrome extraction cycle (including gate-measurement-reset correlations) is central to the noise-informed decoder, yet no cross-validation against observed syndrome statistics or syndrome histogram comparisons is described to confirm predictive accuracy.

Authors: The referee is correct that explicit validation of the ACES model against experimental syndrome statistics strengthens the claim. Although ACES is constructed to extract context-dependent error rates for the entire syndrome cycle, we did not include a direct comparison of predicted versus observed syndrome histograms in the original submission. We have now added this cross-validation in the revised experimental results section, demonstrating quantitative agreement between the ACES-inferred error model and the measured syndrome distributions. revision: yes
Referee: [Decoder and post-selection description] Decoder and post-selection description: without quantified acceptance rates or a side-by-side logical error rate comparison on the same dataset with and without leakage post-selection, it is unclear whether the 38.3% figure is load-bearing or could be materially altered by the filtering bias.

Authors: We acknowledge that the original text did not quantify the acceptance rate or present an explicit with/without comparison for the leakage post-selection step. The 38.3% improvement is obtained with the full pipeline, but to address the concern we have added the measured acceptance fraction and a direct comparison of logical error rates (on identical experimental shots) with and without the post-selection filter in the revised decoder and post-selection description. This clarifies the relative contributions of the noise-informed decoder and the leakage-exclusion step. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental results from independent hardware measurements and ACES sampling

full rationale

The paper reports an experimental implementation of a distance-5 dynamic compass code on superconducting hardware. The claimed 38.3% logical error rate improvement is obtained directly from measured syndrome statistics after ACES-based noise characterization and soft-information post-selection. No equations, derivations, or predictions are presented that reduce by construction to fitted parameters, self-definitions, or self-citation chains. The central result is an empirical outcome on physical hardware rather than a mathematical reorganization of inputs. Any prior self-citations on code construction or ACES methodology are non-load-bearing for the reported experimental improvement.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum mechanics and the assumption that the heavy-hex connectivity matches the physical device; no free parameters, invented physical entities, or ad-hoc axioms beyond domain-standard quantum error correction assumptions are introduced in the abstract.

axioms (1)

domain assumption The physical qubit array follows heavy-hex lattice connectivity.
The code and syndrome extraction are explicitly designed for this connectivity, which is a standard assumption for the target superconducting hardware.

pith-pipeline@v0.9.0 · 5524 in / 1325 out tokens · 57496 ms · 2026-05-10T13:10:03.818301+00:00 · methodology

discussion (0)

Reference graph

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