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arxiv: 2604.14296 · v2 · pith:YX6NEGLNnew · submitted 2026-04-15 · 🪐 quant-ph

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
show 2 more authors
Robin Harper Benjamin J. Brown
This is my paper

Pith reviewed 2026-05-21 09:27 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum error correctionheavy-hex latticesubsystem codedynamic compass codenoise-informed decodingaveraged circuit eigenvalue samplingsuperconducting qubitslogical error rate
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The pith

The dynamic compass code enables scalable quantum error correction on heavy-hex lattices with a novel syndrome extraction cycle and noise-informed decoding.

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

This paper introduces the dynamic compass code as a subsystem code tailored for qubits on a heavy-hex lattice, featuring a new way to extract error syndromes that uses qubits efficiently while holding a competitive error threshold. The authors test a distance-5 version on a real superconducting array and feed in detailed device noise data from averaged circuit eigenvalue sampling to improve the decoder. They also use soft measurement outputs to spot leakage and apply post-selection. A reader would care because this shows how to match error correction to actual hardware constraints rather than assuming uniform noise, which could help move toward larger fault-tolerant systems.

Core claim

The dynamic compass code is a subsystem code with a novel syndrome extraction cycle that achieves competitive thresholds while making efficient use of qubits on a heavy-hex lattice. When implemented at distance 5 on a superconducting device, incorporating context-dependent error rates from averaged circuit eigenvalue sampling, soft measurement information, and leakage post-selection improves the logical error rate by up to 38.3 percent.

What carries the argument

The dynamic compass code's novel syndrome extraction cycle, which extracts syndromes in a pattern adapted to the heavy-hex geometry and supports direct use of per-element noise rates in decoding.

If this is right

  • The code remains efficient when scaled to larger distances on the same heavy-hex layout.
  • Device-specific noise data from averaged circuit eigenvalue sampling can be plugged directly into the decoder for better performance.
  • Soft information from measurements allows reliable detection and exclusion of leakage events via post-selection.
  • The overall approach yields measurable reductions in logical error rates under realistic hardware noise.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar tailored codes and noise-characterization steps could be developed for other qubit connectivities beyond heavy-hex.
  • Integrating leakage-aware post-selection with standard decoders may become standard practice for near-term quantum error correction experiments.
  • The method suggests testing whether the same noise-informed gains appear when logical gates are added to the code.

Load-bearing premise

The averaged circuit eigenvalue sampling procedure supplies accurate context-dependent error rates for every element of the syndrome extraction cycle that the decoder can use directly without selection bias or unaccounted leakage.

What would settle it

An experiment on the distance-5 code where the logical error rate with the full noise-informed decoder and post-selection shows no improvement over a baseline decoder using only uniform error assumptions would falsify the claimed benefit.

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 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 7
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-by￾shot 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.

Referee Report

2 major / 2 minor

Summary. The paper introduces the dynamic compass code, a subsystem code with a novel syndrome extraction cycle optimized for heavy-hex qubit lattices. It reports an experimental distance-5 implementation on a superconducting qubit array that uses averaged circuit eigenvalue sampling (ACES) to obtain context-dependent error rates, augments the decoder with soft measurement information, and applies leakage post-selection, claiming up to a 38.3% reduction in logical error rate.

Significance. If the noise-informed improvements hold without bias from post-selection, the work demonstrates a practical route to tailoring quantum error correction to measured device noise on a scalable lattice geometry. The distance-5 experimental demonstration provides concrete data on how ACES-derived rates and soft information can enhance decoder performance, which is a useful contribution to hardware-aware QEC even if the precise magnitude of the gain requires further controls.

major comments (2)
  1. [Abstract and experimental results] Abstract and experimental results section: The central 38.3% logical-error-rate improvement for the distance-5 dynamic compass code is load-bearing on the assumption that ACES supplies unbiased, context-dependent error rates for the post-selected ensemble. No control experiment is described that recomputes the logical error rate on the post-selected shots using the original (non-ACES) decoder; without this, it remains unclear whether the reported gain is attributable to better noise modeling or to the filtering step itself.
  2. [Code definition and threshold analysis] Code definition and threshold analysis: The precise syndrome-extraction cycle of the dynamic compass code and the derivation of its claimed competitive threshold are not presented with sufficient detail (e.g., no explicit stabilizer or gauge-operator schedule or numerical threshold calculation) to allow independent assessment of the code's properties separate from the experimental noise tailoring.
minor comments (2)
  1. [Methods] The ACES protocol description would benefit from an explicit statement of how the sampled eigenvalues are mapped onto the decoder's error model and whether any regularization or truncation is applied.
  2. [Figures] Figure captions for logical-error-rate plots should state the total number of shots, the post-selection fraction retained, and whether error bars represent statistical or systematic uncertainty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. Their comments highlight important points regarding experimental controls and code presentation that we address below. We have prepared revisions to strengthen the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and experimental results] Abstract and experimental results section: The central 38.3% logical-error-rate improvement for the distance-5 dynamic compass code is load-bearing on the assumption that ACES supplies unbiased, context-dependent error rates for the post-selected ensemble. No control experiment is described that recomputes the logical error rate on the post-selected shots using the original (non-ACES) decoder; without this, it remains unclear whether the reported gain is attributable to better noise modeling or to the filtering step itself.

    Authors: We agree that an explicit control would better isolate the contribution of the ACES-informed decoder from post-selection effects. In the revised manuscript we will add this control by re-decoding the post-selected shots with the baseline (non-ACES) decoder and reporting the resulting logical error rates alongside the noise-tailored results. This comparison will confirm that the observed improvement stems from the context-dependent error rates rather than the leakage post-selection step alone. The post-selection itself uses soft measurement information to flag leakage events and is applied uniformly; the new control will quantify its interaction with the tailored decoder. revision: yes

  2. Referee: [Code definition and threshold analysis] Code definition and threshold analysis: The precise syndrome-extraction cycle of the dynamic compass code and the derivation of its claimed competitive threshold are not presented with sufficient detail (e.g., no explicit stabilizer or gauge-operator schedule or numerical threshold calculation) to allow independent assessment of the code's properties separate from the experimental noise tailoring.

    Authors: We acknowledge that additional detail is required for independent verification. In the revision we will expand the code-definition section to include the full stabilizer and gauge-operator measurement schedule for the dynamic compass code's syndrome-extraction cycle. We will also report the numerical threshold calculation, specifying the depolarizing noise model, Monte-Carlo simulation parameters, and the obtained threshold value with statistical uncertainty. These additions will allow readers to assess the code's intrinsic properties independently of the experimental noise tailoring. revision: yes

Circularity Check

0 steps flagged

No significant circularity: experimental results tied to measured device noise

full rationale

The paper introduces the dynamic compass code as a new subsystem code and reports experimental implementation of a distance-5 instance on superconducting qubits. Logical error rate improvements (up to 38.3%) are obtained by feeding ACES-characterized context-dependent error rates and soft measurement information into the decoder, with leakage post-selection. These gains are directly measured outcomes on hardware rather than any mathematical derivation, fitted parameter, or self-citation that reduces the central claim to its own inputs by construction. No equations or steps in the provided text exhibit self-definitional, fitted-input-called-prediction, or load-bearing self-citation patterns. The work is self-contained against external benchmarks (device measurements) and receives the default low-circularity finding for primarily experimental papers.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard quantum mechanics, the validity of the ACES noise model, and the assumption that post-selection on leakage does not bias the logical error rate measurement.

axioms (1)
  • standard math Standard assumptions of quantum mechanics and Markovian noise in superconducting qubits
    Underlying framework invoked for all error correction analysis.
invented entities (1)
  • dynamic compass code no independent evidence
    purpose: Subsystem code with novel syndrome extraction cycle for heavy-hex lattice
    New code construction introduced by the authors.

pith-pipeline@v0.9.0 · 5755 in / 1275 out tokens · 34560 ms · 2026-05-21T09:27:18.812171+00:00 · methodology

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