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arXiv:2607.25865

OmniQEC: discovering practical quantum error-correcting codes by an AI scientist

Ge Yan, Shanchuan Li, Pengyue Ma, Qixin Zhang, Pingchuan Ma, Jianping Wang, Min-Hsiu Hsieh, Yuxuan Du

quant-phcs.AIcs.MASubmitted Jul 28, 2026• Announced Jul 29, 2026• 0 citations
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Abstract

Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and $14$ total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with $[\![72,12,6]\!]$ and $[\![144,12,12]\!]$ under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.

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Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and 141414 total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with [ ⁣[72,12,6] ⁣][\![72,12,6]\!][[72,12,6]] and [ ⁣[144,12,12] ⁣][\![144,12,12]\!][[144,12,12]] under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.
Scalable quantum computation is expected to rely on fault-tolerant quantum computation (FTQC), in which quantum error correction (QEC) suppresses physical errors sufficiently to support reliable logical operations. This requires quantum compilation to move beyond general-purpose circuit optimization toward encoding-aware and protocol-structured compilation across the full stack of fault-tolerant quantum computers. Beyond circuit synthesis and hardware mapping, an FTQC compiler must lower algorithm-level operations into the logical gate set supported by the chosen code, coordinate encoded data and ancilla resources, realize logical operations together with repeated syndrome extraction under hardware constraints, and provide the resulting measurement stream to real-time decoding. This survey presents a full-stack view of compiler design for QEC-protected quantum computation. We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and decoder runtime integration. At the logical level, we review surface-code lattice-surgery compilers, beyond-surface-code code-surgery frameworks including emerging qLDPC approaches, and compilation support for non-Clifford operations such as magic-state distillation and code switching. At the physical level, we survey hardware-aware QEC realization on superconducting, trapped-ion, and neutral-atom platforms. We further examine decoder models, real-time decoding systems, and frame-management mechanisms that close the feedback loop during fault-tolerant execution. Finally, we identify open challenges in cross-layer optimization, qLDPC compilation, compiler-decoder co-design, runtime adaptivity, and the development of integrated and benchmarkable FTQC compilation stacks. An actively maintained paper list is available at: github.com/chenghongz/QEC-compiler-design.
Quantum computers promise computational advantages for many important problems across various application domains. Unfortunately, physical quantum devices are highly susceptible to errors that limit us from running most of these quantum applications. Quantum Error Correction (QEC) codes are required to implement Fault-Tolerant Quantum Computers (FTQC) on which computations can be performed without encountering errors. Error decoding is a critical component of quantum error correction and is responsible for transforming a set of qubit measurements generated by the QEC code, called the syndrome, into error locations and error types. For the feasibility of implementation, error decoders must not only identify errors with high accuracy, but also be fast and scalable to a large number of qubits. Unfortunately, most of the prior works on error decoding have focused primarily only on the accuracy and have relied on software implementations that are too slow to be of practical use. Furthermore, these studies only look at designing a single decoder and do not analyze the challenges involved in scaling the storage and bandwidth requirements when performing error correction in large systems with thousands of qubits.In this paper, we present AFS, an accurate, fast, and scalable decoder architecture that is designed to operate in the context of systems with hundreds of logical qubits. We present the hardware implementation of AFS, which is based on the Union Find decoding algorithm and employs a three-stage pipelined design. AFS provides orders of magnitude higher accuracy compared to recent SFQ-based hardware decoders (logical error rate of 6×10−10for physical error rate of 10−3) and low decoding latency (42ns on average), while being robust to measurement errors introduced while extracting syndromes during the QEC cycles. We also reduce the amount of decoding hardware required to perform QEC simultaneously on all the logical qubits by co-designing the micro-architecture across multiple decoding units. Our proposed Conjoined-Decoder Architecture (CDA) reduces the storage overhead by 70% (10MB to 2.8MB). Finally, we reduce the bandwidth overheads required to transmit syndromes from the qubits to the decoders by exploiting the sparsity in the syndromes and compressing the data. Our proposed Syndrome Compression reduces the bandwidth requirement by 30x, on an average.
Quantum error correction (QEC) is transitioning from physical feasibility demonstrations to systems engineering challenges. Google has achieved below-threshold performance on distance-5/7 surface codes, while Riverlane and Rigetti have demonstrated hardware-integrated low-latency feedback loops. These milestones indicate that the core challenge of real-time decoding has shifted from algorithmic capability to system-level engineering. However, a substantial engineering gap remains between laboratory demonstrations and scalable fault-tolerant quantum computing (FTQC). This white paper addresses three questions: (1) Where are the real bottlenecks in real-time QEC: beyond average decoder speed, the constraints lie in QEC round time, tail latency, and end-to-end data path coordination; (2) How mature are mainstream decoder algorithms: we benchmark the major decoders for both surface codes and quantum low-density parity-check (qLDPC) codes, evaluating their real-time readiness; (3) What system stack do we propose: a six-layer reference architecture from syndrome acquisition to logical operations, with interface definitions and latency budget models. Our results quantify the gap between current decoder performance and real-time requirements, and identify the architectural choices needed to close it.
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the [144,12,12][144, 12, 12][144,12,12] Gross code, the decoder achieves logical error rates up to ∼17\sim 17∼17x below existing decoders - reaching logical error rates ∼10−10\sim 10^{-10}∼10−10 at physical error p=0.1%p=0.1\%p=0.1% - with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.
Quantum error correction (QEC) represents the cornerstone technology for realizing fault-tolerant quantum computing, addressing the fundamental challenge of quantum state decoherence in noisy intermediate-scale quantum (NISQ) devices. This comprehensive review examines recent advances in QEC implementations from 2020-2024, spanning theoretical foundations to practical hardware demonstrations. We analyze the evolution from pioneering stabilizer codes to modern topological approaches, with particular emphasis on surface codes and low-density parity-check (LDPC) codes that have demonstrated below-threshold error correction in superconducting and trapped-ion systems. The paper provides a comparative analysis of classical and machine learning-based decoder algorithms, evaluating their performance through complexity analysis and threshold comparisons in real-time error correction scenarios. Through examination of breakthrough experiments by Google, IBM, Quantinuum, and emerging platforms, we assess the current state of fault-tolerant quantum computing and identify critical engineering challenges including correlated noise models, cryogenic control systems, and scalable logical gate implementations. Our quantitative analysis reveals that while significant progress has been made toward practical fault-tolerance thresholds, achieving the resource efficiency and reliability required for large-scale quantum computation remains challenging. We provide detailed resource estimates for key applications including Shor's algorithm and optimization problems, along with analysis of industry roadmaps toward thousand-logical-qubit systems. This review serves as a comprehensive guide for researchers and engineers working toward the next generation of fault-tolerant quantum computers, with particular focus on information-theoretic perspectives relevant to quantum information entropy and syndrome processing.
Quantum error correction (QEC) represents the cornerstone technology for realizing fault-tolerant quantum computing, addressing the fundamental challenge of quantum state decoherence in noisy intermediate-scale quantum (NISQ) devices. This comprehensive review examines recent advances in QEC implementations from 2020-2024, spanning theoretical foundations to practical hardware demonstrations. We analyze the evolution from pioneering stabilizer codes to modern topological approaches, with particular emphasis on surface codes and low-density parity-check (LDPC) codes that have demonstrated below-threshold error correction in superconducting and trapped-ion systems. The paper provides a comparative analysis of classical and machine learning-based decoder algorithms, evaluating their performance through complexity analysis and threshold comparisons in real-time error correction scenarios. Through examination of breakthrough experiments by Google, IBM, Quantinuum, and emerging platforms, we assess the current state of fault-tolerant quantum computing and identify critical engineering challenges including correlated noise models, cryogenic control systems, and scalable logical gate implementations. Our quantitative analysis reveals that while significant progress has been made toward practical fault-tolerance thresholds, achieving the resource efficiency and reliability required for large-scale quantum computation remains challenging. We provide detailed resource estimates for key applications including Shor's algorithm and optimization problems, along with analysis of industry roadmaps toward thousand-logical-qubit systems. This review serves as a comprehensive guide for researchers and engineers working toward the next generation of fault-tolerant quantum computers, with particular focus on information-theoretic perspectives relevant to quantum information entropy and syndrome processing.