Hugo Théveniaut, Evert van Nieuwenburg
We investigate the use of the evolutionary NEAT algorithm for the optimization of a policy network that performs quantum error decoding on the toric code, with bitflip and depolarizing noise, one qubit at a time. We find that these NEAT-optimized network decoders have similar performance to previously reported machine-learning based decoders, but use roughly three to four orders of magnitude fewer parameters to do so.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Quantum low-density parity-check codes can be decoded using a syndrome based $\mathrm{GF}(4)$ belief propagation decoder. However, the performance of this decoder is limited both by unavoidable $4$-cycles in the code's factor graph and the degenerate nature of quantum errors. For the subclass of CSS codes, the number of $4$-cycles can be reduced by breaking an error into an $X$ and $Z$ component and decoding each with an individual $\mathrm{GF}(2)$ based decoder. However, this comes at the expense of ignoring potential correlations between these two error components. We present a number of mod…
An Analysis of Speculative Window Decoders for Quantum Error Correction
研究推测性窗口解码在慢速门下的性能，分析其对推测精度、解码延迟、处理器数量和并行度的敏感性，提出设计原则并揭示非推测解码器优于推测解码器的条件。
Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a decoder that employs a neural network to calculate the conditional distribution, then sample from the distribution - the sample will be the predicted error for the given syndrome. We present an implementation of such an algorithm that can be applied to any stabilizer code. Testing it on the toric code, it has higher threshold than a number of known decoders thanks…
Simpler encoding and decoding networks are necessary for more reliable quantum error correcting codes (QECCs). The simplification of the encoder-decoder circuit for a perfect five-qubit QECC can be derived analytically if the QECC is converted from its equivalent one-way entanglement purification protocol (1-EPP). In this work, the analytical method to simplify the encoder-decoder circuit is introduced and a circuit that is as simple as the existent simplest circuits is presented as an example. The encoder-decoder circuit presented here involves nine single- and two-qubit unitary operations, o…
Proof of a finite threshold for the union-find decoder
本文证明了表面码上联合查找解码器的有限阈值，通过改进的误差聚类框架，提供了理论基础并统一了容错研究框架。
Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check (LDPC) codes with a loss function tailored to error degeneracy. Training substantially improves the performance of BP decoders for all families of codes we tested and may solve the degeneracy problem which plagues the decoding of quantum LDPC codes.
Optimization of decoder priors for accurate quantum error correction
本文提出一种受强化学习启发的解码器先验校准方法，通过最小化逻辑错误率，在Google Sycamore处理器上使重复码和表面码解码精度分别提升16%和3.3%，为量子纠错性能优化提供关键工具。
Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error events were extracted using fast, mid-circuit measurements and resets of the physical qubits. Among the error decoders we considered, we introduce a perfect matching decoder that was calibrated from measurements containing up to size-4 correlated events. To compare the decoders, we used a partial post-selection scheme shown to retain ten times more data than ful…
A Practical and Scalable Decoder for Topological Quantum Error Correction with Digital Annealer
提出一种基于Fujitsu Digital Annealer的量子纠错解码器，将稳定子码纠错映射为QUBO问题求解，实验表明其计算扩展性优于SA和MWPM，阈值接近MWPM且硬件实现优于UF解码器。
Decoder Switching: Breaking the Speed-Accuracy Tradeoff in Real-Time Quantum Error Correction
针对实时量子纠错中速度与精度的权衡难题，提出解码器切换框架，结合强弱解码器按需切换，实现精度媲美强解码器、速度比肩弱解码器的效果，还配套双窗口解码方案，为可扩展实时解码设备铺路。
Neural network decoder for near-term surface-code experiments
本文研究用于小码距表面码的神经网络解码器，结合 transmon 处理器实验与模拟数据，证明其利用相关错误和模拟软信息可显著降低逻辑错误率。
The END: An Equivariant Neural Decoder for Quantum Error Correction
本文针对量子纠错解码代价随系统规模指数增长的问题，提出一种利用环面码对称性的等变神经解码器END，以数据高效方式实现最优解码近似，并取得超越以往神经解码器的最先进准确率。
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decodin…
Design of a Quantum Error Correction Decoder Exploiting Temporal Parallelism
本研究提出利用时间并行性实现结合Union-Find算法的三明治译码方法的微架构及ASIC实现，可降低量子纠错译码延迟并保持逻辑错误阈值。
Zero-G: A Pre-Decoder-Aware Decoder for Quantum Error Correction
针对现有量子纠错主解码器无法利用预解码稀疏性的问题，提出Zero-G解码器，其可动态权衡延迟与精度，实现10倍延迟提升，支持CPU和FPGA异构部署，适配大码距与多逻辑量子比特场景。
Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the classical electronic back-end. Decoders employing neural networks (NN) are well-suited for this task but their hardware implementation has not been presented yet. This work presents a space exploration of fully-connected feed-forward NN decoders for small distance surface codes. The goal is to optimize the neural network for high decoding performance, while keeping…
Designing Quantum Error Correcting Codes to fit decoders via Reinforcement Learning
该研究提出强化学习方法协同设计量子纠错码稳定器集合与译码器，固定译码器架构后用近端策略优化训练智能体，在去极化信道噪声下最大化译码器性能，可生成适配译码器的双变量自行车码。
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this paper we introduce two renormalization group decoders for qudit codes and analyze their error correction thresholds and efficiency. The first decoder is a generalization of a "hard-decisions" decoder due to Bravyi and Haah [arXiv:1112.3252]. We modify this decoder to overcome a percolation effect which limits its threshold performance for high dimensions. The s…
Analyzing Decoders for Quantum Error Correction
本文提出一种系统方法评估量子纠错解码器，通过形式语义和优化技术提高解码器准确性和鲁棒性，优于传统模拟方法，尤其在低错误率情况下表现更佳。
Diversity Methods for Improving Convergence and Accuracy of Quantum Error Correction Decoders Through Hardware Emulation
本文提出一种硬件仿真器评估量子纠错解码器性能，结合不同量化级别的信念传播解码器，提升量子低密度奇偶校验码的解码效率与准确性。
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical evidence for thresholds against Pauli errors for bulk qubits. We compare the performance of holographic code families of various code rates and find phenomenological Pauli error thresholds ranging from $7\%$ to $16\%$, depending on the code rate. Additionally we give numerical evidence that specific distance measures of the codes we consider scales polynomially…
Breadth-first graph traversal union-find decoder
本文开发了并查集解码器变体，简化实现并提升解码速度，可处理量子比特擦除和泡利错误，适用于非拓扑qLDPC码，并在多个码上进行了基准测试。
Enhancing the Clique Local Decoder to Correct Length-2 Space Errors in the Surface Code
本文提出 Clique_L2 局部解码器，通过放宽约束并增加低成本逻辑来纠正表面码中长度为 2 的空间错误链，相比 Clique_L1 最高可将解码带宽降低 18.3 倍。
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes the operations needed to correct or compensate for the errors according to the measured syndrome, even when the measurement itself is error prone. Previously decoders based on minimum-weight perfect matching have been studied. However, these are not immediately generalizable from qubit to qudit codes. In this work, we develop a fault-tolerant decoder for the …
Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strenghts of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size $L$ from $Θ(L^{2/3})$ to $Ω(L^{1-ε})$ for any $ε…
Testing the Accuracy of Surface Code Decoders
本文提出首个系统性技术，通过将查找表解码器与算法解码器在距离高达七的表面码上进行对比，测试不同量子纠错码解码方案的准确性与有效性，为数据驱动的混合解码器定制设计奠定基础。
Self-attention U-Net decoder for toric codes
本文提出自注意力 U-Net 量子解码器（SU-NetQD）用于环面码，在电路级噪声下优于 MWPM，获得 0.231 高阈值，结合低层与高层解码器及迁移学习实现可扩展高精度解码。
We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We also numerically benchmark the performance of the decoder in the setting with measurement errors using various noise models. We find that this error correction procedure is remarkably robust against measurement errors and is al…
A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within the limitations on communication that are imposed by the physical architecture. To this end we propose a local `pre-decoder', which makes greedy corrections to reduce the amount of syndrome data sent to a standard matching decoder. We study these classical overheads for the surface code under a phenomenological phase-flip noise model with imperfect measurement…
Tesseract: A Search-Based Decoder for Quantum Error Correction
Tesseract是一种基于A*搜索的最可能错误解码器，用于低密度奇偶校验量子纠错码，在保持准确性的同时显著提速，并发现二变量自行车码比表面码更高效。
Fooling the Decoder: An Adversarial Attack on Quantum Error Correction
本文提出一种针对强化学习表面码解码器 DeepQ 的白盒对抗攻击，通过选择使 Q 函数最悲观的症状体积，将逻辑量子比特寿命从约 10^5 周期降至 60，并确认该效应源于对物理可实现错误配置的选择，首次实现对机器学习 QEC 解码器的对抗攻击。
The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general principles for building quantum decoders from classical decoders. Given any pair of classical codes, we can build a quantum code using the hypergraph product, yielding a hypergraph product code. Here we show we can also lift the decoders for these classical codes. That is, given oracle access to a minimum weight decoder for the relevant classical codes, the corre…
Optimal Decoder for the Error Correcting Parity Code
本文提出奇偶码的两步解码器，在无噪测量下可实现近优乃至最优解码，含噪测量下容错阈值超5%，为强噪声偏置量子比特平台验证量子优势提供了可行方案。
The error rates of quantum devices are orders of magnitude higher than what is needed to run most quantum applications. To close this gap, Quantum Error Correction (QEC) encodes logical qubits and distributes information using several physical qubits. By periodically executing a syndrome extraction circuit on the logical qubits, information about errors (called syndrome) is extracted while running programs. A decoder uses these syndromes to identify and correct errors in real time, which is required to use feedback implemented in quantum algorithms. Unfortunately, software decoders are slow an…
Minimum-Weight Parity Factor Decoder for Quantum Error Correction
针对量子纠错中MLE解码在通用qLDPC码上难解的问题，提出统一框架HyperBlossom，将其建模为MWPF问题并推广blossom算法到超图，实现的Hyperion软件在解码精度和运行效率上均优于现有解码器。
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold maximum-likelihood decoders require an explicit error model for Pauli errors to decode a specific syndrome, whereas lower-threshold heuristic approaches such as minimum weight matching are "error agnostic". Here we consider an intermediate approach, formulating a decoder that depends on the bias, i.e., the relative probability of phase-flip to bit-flip errors, but …
Minimising surface-code failures using a color-code decoder
本文将 surface code 的 syndrome 映射到 color code，以复用更先进的 color-code 解码器，从而校正 depolarising 误差，并在逻辑错误率上获得指数级改善。
There has been a rise in decoding quantum error correction codes with neural network based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger code distances due to an exponential increase of the error syndrome space. Note that, successfully decoding the surface code under realistic noise assumptions will limit the size of the code to less than 100 qubits with current neural network based decoders. Such a problem can be tackled by a distributed way of decoding, similar to the Renormalization Group (RG…
Lower Bounds on Error Exponents via a New Quantum Decoder
本文提出一种基于替代矩阵商的新型量子解码器，并据此为经典-量子及纠缠辅助信道编码的单次与渐近错误指数建立 Rényi 互信息下界。
Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for practical scalable quantum error correction and require efficient and scalable decoders. In this work, we propose and study the efficiency of a decoder for 2D topological color codes on the 4.8.8 lattice, by building on the work of [1] for color codes on hexagonal lattices. The decoder is based on a rescaling approach, in which syndrome information on a part…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that they can be evaluated by dedicated hardware which is very fast and consumes little power. Machine learning has been previously applied to decode the surface code. However, these approaches are not scalable as the training has to be redone for every system size which becomes increasingly difficult. In this work the existence of local decoders for higher dimensi…
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent to a boundary. We numerically estimate a threshold of $4\% - 8\%$ for Pauli $X$ errors and a threshold of $0.7\% - 0.8\%$ for Pauli $Z$ errors. Our work is a first step towards characterizing the performance of Bombín's recently proposed "colorful quantum computing."
We present a decoder for nonbinary CWS quantum codes using the structure of union codes. The decoder runs in two steps: first we use a union of stabilizer codes to detect a sequence of errors, and second we build a new code, called union code, that allows to correct the errors.
The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar color code with a triangular boundary where we match syndrome defects on a nontrivial manifold that has the topology of a Möbius strip. A basic implementation of our decoder used on the color code with hexagonal lattice geometry demonstrates a logical failure rate that is competitive with the optimal performance of the surface code, $\sim p^{α\sqrt{n}}$, wit…
Neural Decoders for Universal Quantum Algorithms
针对量子算法解码中ML解码器应用受限的问题，提出模块化注意力神经解码器，可学习门控错误关联并泛化到多类场景，在多种纠错码下达到SOTA，兼具可解释性，为容错量子计算提供实用工具。
SAQ: Stabilizer-Aware Quantum Error Correction Decoder
本文提出SAQ解码器，结合Transformer学习与约束感知后处理，实现接近最大似然准确率和线性计算可扩展性，优于现有神经和经典方法。
Analysis of the Error-Correcting Radius of a Renormalisation Decoder for Kitaev's Toric Code
本文针对Kitaev环面码的重整化解码器，研究其在最坏情况或对抗性错误下的纠错半径，证明其能纠正权重小于$\frac{5}{6} d^{\log_{2}(6/5)}$的所有错误模式，并给出权重按$d^{1/2}$缩放的不可纠正错误模式。
Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error correction is required to execute a useful quantum algorithm. The decoder is a key component of the error correction scheme whose role is to identify errors faster than they accumulate in the quantum computer and that must be implemented with minimum hardware resources in order to scale to the regime of practical applications. In this work, we consider surfa…
Scalable Neural Decoders for Practical Real-Time Quantum Error Correction
针对Transformer神经解码器复杂度高、实时性不足的问题，本文提出基于Mamba状态空间模型的解码器，复杂度降至O(d²)，在模拟实时场景中错误阈值达0.0104，优于Transformer的0.0097，兼顾速度与精度。
Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes
本文提出了一种基于缺陷中心的稀疏Mamba解码器，通过仅处理活跃的检测事件，提高了量子纠错中表面码syndrome处理的效率和准确性，同时在多个基准测试中展示了显著的性能提升。
High-performance local decoders for defect matching in 1D
提出一维量子重复码的两种新型局部解码器，通过信号规则与剪切规则显著缩小与全局解码器的性能差距，实现指数级逻辑错误抑制并降低实现要求。
Trapping Sets of Detector Error Models
本研究提出基于陷阱集的框架，可预测量子纠错迭代解码器的错误平层，揭示码距与解码性能的差距，为解码算法设计提供指导。
Due to the low error tolerance of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing. Surface code (SC) associated with its decoding algorithm is one of the most promising quantum error correction (QEC) methods. % One of the challenges of QEC is its high complexity and computational demand. QEC needs to be very power-efficient since the power budget is limited inside of a dilution refrigerator for superconducting qubits by which one of the most successful quantum computers (QCs) is built. In this paper, we propose an online-QEC algorithm and its ha…
With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up to larger quantum circuits which in turn will require fast and scalable algorithms for quantum error correction. Here we present a neural network based decoder that, for a family of stabilizer codes subject to depolarizing noise and syndrome measurement errors, is scalable to tens of thousands of qubits (in contrast to other recent machine learning inspired…
Decoder-Prior Poisoning in Quantum Error Correction: Attacks and PriorGuard Defense
针对量子纠错解码器先验更新路径的投毒攻击，提出PriorGuard轻量级语义防护，仅投毒6.4%先验条目可致逻辑错误率提升3.35倍，防护以低误报率恢复损失。
A Unified Hardware-to-Decoder Architecture for Hybrid Continuous-Variable and Discrete-Variable Quantum Error Correction in LiDMaS+
本文提出一种统一的硬件到解码器架构，用于LiDMaS+中的混合连续变量和离散变量量子纠错，通过标准化记录并复现实验结果，验证了不同解码器在不同操作模式下的性能差异。
GAN decoder on a quantum toric code for noise-robust quantum teleportation
本文提出基于GAN的量子拓扑码解码器，通过特征值数据集训练生成器和判别器，将解码伪阈值从经典方法的约0.1099提升至约0.2108，并显著增强退极化噪声下量子隐形传态的保真度。
We present an AI-based decoding agent for quantum error correction of depolarizing noise on the toric code. The agent is trained using deep reinforcement learning (DRL), where an artificial neural network encodes the state-action Q-values of error-correcting $X$, $Y$, and $Z$ Pauli operations, occurring with probabilities $p_x$, $p_y$, and $p_z$, respectively. By learning to take advantage of the correlations between bit-flip and phase-flip errors, the decoder outperforms the minimum-weight-perfect-matching (MWPM) algorithm, achieving higher success rate and higher error threshold for depolari…
Decoding quantum low density parity check codes with diffusion
本文提出基于扩散模型的量子LDPC码解码器，利用掩码扩散机制从综合征推断逻辑错误，在双变量自行车码上超越BP-OSD和自回归解码器，兼具高精度与速度优势。
Calibration-Conditioned FiLM Decoders for Low-Latency Decoding of Quantum Error Correction Evaluated on IBM Repetition-Code Experiments
基于IBM重复码实验，该校准条件下的FiLM解码器在低延迟下显著降低逻辑错误率，展示出适应性解码的潜力。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。