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arxiv: 2605.00038 · v2 · submitted 2026-04-28 · 💻 cs.AR · quant-ph

Recognition: unknown

Lottery BP: Unlocking Quantum Error Decoding at Scale

Yanzhang Zhu , Chen-Yu Peng , Yun Hao Chen , Yeong-Luh Ueng , Di Wu
Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:42 UTC · model grok-4.3

classification 💻 cs.AR quant-ph
keywords quantum error correctionbelief propagationdecodingtopological codessurface codetoric codescalable architecture
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0 comments X

The pith

Introducing randomness into belief propagation decoding raises accuracy for topological quantum codes by 2 to 8 orders of magnitude.

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

This paper seeks to bridge the gap between existing quantum error decoders that fall short in accuracy, speed, generality, or scalability and an ideal decoder suitable for fault-tolerant quantum computing with millions of qubits. Lottery BP adds randomness to the belief propagation process to achieve much higher accuracy on topological codes like surface and toric codes. Syndrome vote pre-processing compresses multi-round syndromes to ease the backlog issue. The PolyQec architecture uses Lottery BP locally to invoke the global ordered statistics decoder far less often. A new GPU-based simulator called Syndrilla enables fair and fast evaluation of such decoders.

Core claim

Lottery BP introduces randomness during belief propagation decoding, improving accuracy over standard BP by 2 to 8 orders of magnitude for topological codes. Syndrome vote serves as a pre-processing step to handle multi-round measurement errors by compressing syndromes. The PolyQec architecture implements Lottery BP as a local decoder paired with ordered statistics decoding as global, reducing the need for the costly global step by 3 to 5 orders of magnitude while remaining configurable for different codes and check types.

What carries the argument

Lottery BP, the decoder that introduces randomness into belief propagation iterations to enhance convergence and accuracy on quantum error correction codes.

If this is right

  • Real-time decoding becomes possible for large-scale quantum systems with millions of qubits.
  • The backlog problem from accumulating syndromes is mitigated, increasing the time available for decoding.
  • Hybrid decoding architectures can scale better by relying on fast local decoding most of the time.
  • The modular simulator allows rapid development and testing of new decoding methods on GPUs.
  • Configurable designs support both surface/toric codes and X/Z checks in a unified way.

Where Pith is reading between the lines

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

  • If randomness reliably helps BP, similar stochastic elements might improve other iterative algorithms in quantum decoding.
  • Reduced reliance on global decoding could simplify hardware requirements for quantum processors.
  • Further tests on bivariate bicycle codes and other code families would confirm the broad applicability.
  • Integration with neural network decoders might yield even higher performance combinations.

Load-bearing premise

That introducing randomness during BP decoding will reliably boost accuracy across a broad set of codes without introducing new failure modes or excessive computational cost.

What would settle it

A benchmark on a large surface code instance or under a different error model where Lottery BP shows no accuracy gain or slower performance than plain BP.

Figures

Figures reproduced from arXiv: 2605.00038 by Chen-Yu Peng, Di Wu, Yanzhang Zhu, Yeong-Luh Ueng, Yun Hao Chen.

Figure 1
Figure 1. Figure 1: Design space of decoder architecture. The chip size [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: 3D decoding graph for measurement error. Red and [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example of randomness resolving a degenerate deadlock in a [[13,1,3]] surface code. We consider error events occurring [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Lottery policies on surface code at 𝑑 = 9. 10 −3 10 −2 10 0 BP d=3 d=5 d=7 d=9 d=11 d=13 10 −3 10 −2 10 0 Probability Relay BP 10 1 10 3 Iteration count 10 −3 10 −2 10 0 Lottery BP (a) Surface code. 10 −3 10 −2 10 0 BP [[72,12,6]] [[90,8,10]] [[108,8,10]] [[144,12,12]] [[288,12,18]] 10 −3 10 −2 10 0 Probability Relay BP 10 1 10 3 10 5 Iteration count 10 −3 10 −2 10 0 Lottery BP (b) BB code [PITH_FULL_IMAG… view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of decoding iterations at 𝑝 = 0.05. where the middle three variants are adopted in prior works [39]. The resulting accuracy is given in Figure 4a 1 . (1) Global optimal: Among all VNs with the most unsatisfied CNs, flip the sign of the one with the minimum absolute LLR. This policy builds an upper bound but is impractical for hardware implementation due to global search. (2) Global connectivit… view at source ↗
Figure 6
Figure 6. Figure 6: Syndrome vote to handle measurement errors on [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Overview of PolyQec. On the right plane, vertical dashed lines separate each fully pipelined stages [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: CN layout in the memory. whose cost increases quadratically with the code distance. Fortu￾nately, the parity-check matrices of surface and toric codes are regular, which facilitates converting the message layout on the fly instead of storing the parity-check matrix. 2 C2V converter converts the C2V message from CN layout to VN layout, which groups the messages needed by each VN together. On the other hand,… view at source ↗
Figure 9
Figure 9. Figure 9: Resolving read bank conflict of LLR memory. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: outlines Syndrilla. The workflow of Syndrilla is similar to other QEC simulators [14, 15, 53, 57, 64, 71, 76], including error and syndrome generation, followed by decoder and logical check. What distinguishes Syndrilla is integrated metrics to fair evaluation and cross-platform execution for accelerated simulation. Syndrilla also interacts with Stim [30] to support broader error models. Integrated Metric… view at source ↗
Figure 11
Figure 11. Figure 11: Simulating surface code at 𝑑 = 11. CPU and GPU de￾note Syndrilla running on Intel Core i5-13450HX and NVIDIA GeForce RTX 4080. CPU_cpp marks C++ BP+OSD [70] run￾ning on the Intel CPU with no batch support. The runtime represents the total simulation time for each configuration. (a) and (c) have a batch size of 100,000 for BP+OSD and 200,000 for Lottery BP+OSD. (c) and (d) use FP64 data. (d) uses 𝑝 = 0.05.… view at source ↗
Figure 12
Figure 12. Figure 12: Logical error rate without measurement error. [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 15
Figure 15. Figure 15: Quantization on surface code at 𝑑 = 9. 7.1.3 Quantization Analy￾sis. Unlike using floating￾point in simulation, we need to quantize the soft mes￾sages to fixed-point format for efficient hardware imple￾mentation [PITH_FULL_IMAGE:figures/full_fig_p010_15.png] view at source ↗
Figure 14
Figure 14. Figure 14: Invoke rate of OSD [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 18
Figure 18. Figure 18: Scalability study. 7.2.4 Scalability. To support millions of qubits, decoding has to be massively paral￾lel within a tight latency margin due to syndrome generation [29]. An optimal decoder is expected to de￾code as many logical qubits as possible, with minimum area and time. We quantify this advantage using a novel metric, decoding efficiency, defined in Equation 1. Decoding efficiency = Num of decoding … view at source ↗
Figure 17
Figure 17. Figure 17: Area and power at 𝑝 = 10−3 . All BP support 𝑑 ≤ 32. have an SRAM area, since its memory is implemented with register file. All BP variants occupy similar area, with Lottery BP having 0.57𝑚𝑚2 . Among all decoders, Micro Blossom always has the largest area, since it implements the most accurate and costly MWPM. AFS has the smallest area among all, since UF is cheaper to implement and logic area is not repor… view at source ↗
read the original abstract

To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks, suffer from one or more of inaccuracy, costliness, and incompatibility, upon a broad set of quantum error correction codes, such as surface code, toric code, and bivariate bicycle code. Therefore, there exists a gap between existing decoders and an ideal decoder that is accurate, fast, general, and scalable simultaneously. This paper contributes in three aspects, including decoder, decoder architecture, and decoding simulator. First, we propose Lottery BP, a decoder that introduces randomness during decoding. Lottery BP improves the decoding accuracy over BP by 2~8 orders of magnitude for topological codes. To efficiently decode multi-round measurement errors, we propose syndrome vote as a pre-processing step before Lottery BP, which compresses multiple rounds of syndromes into one. Syndrome vote increases the latency margin of decoding and mitigates the backlog problem. Second, we design a PolyQec architecture that implements Lottery BP as a local decoder and ordered statistics decoding (OSD) as a global decoder, and it is configurable for surface/toric code and X/Z check. Since Lottery BP boosts the local decoding accuracy, PolyQec invokes the costly global OSD decoder less frequently over BP+OSD to enhance the scalability, e.g., 3~5 orders of magnitude less for topological codes. Third, to evaluate decoders fairly, we develop a PyTorch-based decoding simulator, Syndrilla, that modularizes the simulation pipeline and allows to extend new decoders flexibly. We formulate multiple metrics to quantify the performance of decoders and integrate them in Syndrilla. Running on GPUs, Syndrilla is 1~2 orders of magnitude faster than CPUs.

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 manuscript proposes Lottery BP, a belief-propagation decoder augmented with randomness injection, claiming 2-8 orders of magnitude higher decoding accuracy than standard BP on topological codes (surface, toric, bivariate bicycle). It introduces syndrome vote as a pre-processor to compress multi-round syndromes, the PolyQec architecture that pairs local Lottery BP with global ordered-statistics decoding (OSD) to reduce OSD invocations, and the Syndrilla PyTorch-based simulator for modular, GPU-accelerated decoder evaluation with multiple performance metrics.

Significance. If the accuracy and scalability claims hold under standard noise models and code distances, the work could meaningfully advance real-time decoding for large-scale quantum error correction by lowering the frequency of expensive global post-processing while providing a reusable simulation framework. The modular Syndrilla simulator is a clear strength for enabling reproducible and extensible decoder comparisons in the field.

major comments (2)
  1. [Abstract] Abstract: The central claim that Lottery BP improves decoding accuracy over BP by 2-8 orders of magnitude is stated without any supporting numerical results, code distances, noise models, logical error rates, or baseline details (e.g., whether comparisons include OSD or not). This is load-bearing for the primary contribution and cannot be assessed from the available information.
  2. [Abstract] Abstract: No ablation is described that isolates the effect of the randomness mechanism in Lottery BP from the syndrome-vote pre-processor or from OSD post-processing. Given well-known BP failure modes on girth-4 quantum LDPC graphs, this omission leaves open whether the reported gains are robust or introduce new variance/cost issues.
minor comments (2)
  1. [Abstract] Abstract: The phrasing 'upon a broad set of quantum error correction codes' is slightly awkward; 'on' would be clearer.
  2. [Abstract] Abstract: The claim that PolyQec invokes OSD '3~5 orders of magnitude less' should specify the exact metric (e.g., invocation rate per logical qubit or per syndrome) and the reference BP+OSD configuration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on the abstract and the importance of clearly isolating contributions. We address each major comment below and outline revisions to improve assessability and robustness.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that Lottery BP improves decoding accuracy over BP by 2-8 orders of magnitude is stated without any supporting numerical results, code distances, noise models, logical error rates, or baseline details (e.g., whether comparisons include OSD or not). This is load-bearing for the primary contribution and cannot be assessed from the available information.

    Authors: We agree that the abstract presents the improvement claim at a high level. The full manuscript details the supporting results in Section 4, including logical error rates for surface, toric, and bivariate bicycle codes at distances d=5 to d=13 under depolarizing and circuit-level noise models. These show 2-8 orders of magnitude gains over standard BP (without OSD post-processing). We will revise the abstract to include a concise example of these metrics, such as the improvement for a representative distance and noise model, to enable immediate assessment. revision: yes

  2. Referee: [Abstract] Abstract: No ablation is described that isolates the effect of the randomness mechanism in Lottery BP from the syndrome-vote pre-processor or from OSD post-processing. Given well-known BP failure modes on girth-4 quantum LDPC graphs, this omission leaves open whether the reported gains are robust or introduce new variance/cost issues.

    Authors: The manuscript includes direct comparisons of Lottery BP to standard BP and evaluates the full PolyQec architecture incorporating syndrome vote and OSD. However, we acknowledge that an explicit ablation isolating the randomness injection would better address concerns about robustness and variance on girth-4 graphs. We will add a dedicated ablation subsection in the revised version, presenting results for Lottery BP variants with and without the randomness mechanism while holding syndrome vote and OSD fixed. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on empirical proposal without self-referential derivations

full rationale

The paper introduces Lottery BP as a new decoder variant that injects randomness into standard belief propagation, then reports measured accuracy gains (2-8 orders) and architectural benefits on specific codes. No equations, parameter fits, uniqueness theorems, or derivation steps appear in the provided text that would allow any claimed result to reduce to its own inputs by construction. The contributions are framed as algorithmic proposals, pre-processing steps, and a simulator implementation, all evaluated externally via simulation rather than derived tautologically. Self-citations are absent from the load-bearing claims, and no 'prediction' is obtained by fitting then renaming. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are specified in the abstract.

pith-pipeline@v0.9.0 · 5648 in / 996 out tokens · 45690 ms · 2026-05-09T20:42:21.498378+00:00 · methodology

discussion (0)

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Reference graph

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