Quantum error correction (QEC) has transitioned from a theoretical promise to an experimental reality, with recent demonstrations of below-threshold logical qubits marking a turning point in the quest for fault-tolerant quantum computing. Over the past five years, breakthroughs in surface code implementations, low-latency decoders, and improved physical qubit fidelities have brought us to the brink of scalable logical qubit systems. Yet the road to practical quantum advantage remains steep: correlated noise, cryogenic control complexity, and the resource overhead of magic state distillation still pose major barriers. Here, we synthesize recent progress across superconductng, trapped-ion, and neutral-atom platforms, assess the state-of the-art in topological and LDPC codes, and highlight engineering challenges that must be overcome to achieve systems with thousands of logical qubits. We argue that the 2025-2035 decade will be decisive for quantum computing, with success hinging on co-design of hardware, software, and algorithms. This perspective outlines a roadmap for the next generation of fault tolerant systems and discusses the societal and economic implications of entering the era of practical quantum advantage.
Quantum error correction (QEC) has transitioned from a theoretical promise to an experimental reality, with recent demonstrations of below-threshold logical qubits marking a turning point in the quest for fault-tolerant quantum computing. Over the past five years, breakthroughs in surface code implementations, low-latency decoders, and improved physical qubit fidelities have brought us to the brink of scalable logical qubit systems. Yet the road to practical quantum advantage remains steep: correlated noise, cryogenic control complexity, and the resource overhead of magic state distillation still pose major barriers. Here, we synthesize recent progress across superconductng, trapped-ion, and neutral-atom platforms, assess the state-of the-art in topological and LDPC codes, and highlight engineering challenges that must be overcome to achieve systems with thousands of logical qubits. We argue that the 2025-2035 decade will be decisive for quantum computing, with success hinging on co-design of hardware, software, and algorithms. This perspective outlines a roadmap for the next generation of fault tolerant systems and discusses the societal and economic implications of entering the era of practical quantum advantage.
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.
Quantum computing has reached a pivotal inflection point with the recent demonstration ofbelow-threshold quantum error correction and the emergence of logical qubits that outperformtheir physical counterparts. This review synthesizes the remarkable progress achieved between2024 and 2026 across multiple quantum hardware platforms, including superconducting circuits,trapped ions, and neutral atom arrays. We examine the theoretical foundations of quantumerror correction codes, with particular emphasis on surface codes and the rapidly advancingquantum low-density parity-check (qLDPC) codes. Key experimental milestones are analyzed,including Google’s Willow chip demonstration of exponential error suppression, IBM’s modularfault-tolerant roadmap culminating in the Starling system, IonQ’s achievement of 48 logicalqubits with a 2:1 encoding ratio, and QuEra’s record-efficiency neutral atom error correctionapproaching the Teraquop regime. The review further explores critical enabling technologiessuch as real-time decoding architectures, magic state distillation protocols, and fault-tolerant gateimplementations. We discuss the remaining challenges in scaling to hundreds of logical qubits,achieving practical logical error rates of 10−10 to 10−15, and realizing end-to-end fault-tolerantalgorithms. By synthesizing these developments, this article provides a comprehensive assessmentof the field’s trajectory toward practical fault-tolerant quantum computing and identifies the keymilestones that will define the next phase of progress.
Quantum error correction (QEC) has emerged as a cornerstone in the quest for scalable and fault-tolerant quantum technologies. While quantum systems promise exponential advantages over classical computation, their extreme susceptibility to noise and decoherence presents a formidable challenge. This review critically examines the trajectory of QEC from its theoretical foundations to recent experimental realizations. Foundational codes, including Shor’s and Steane’s constructions, laid the groundwork for the stabilizer formalism and the development of topological and bosonic codes. Over the past decade, experimental demonstrations have validated these concepts, with logical qubits surpassing the lifetimes of physical qubits on platforms such as superconducting circuits, trapped ions, and photonics. Emerging approaches, including low-density parity-check codes, hybrid mitigation–correction strategies, and artificial intelligence–driven decoders, further illustrate the field’s dynamism. By synthesizing theoretical progress, empirical validation, and cross-platform innovations, this review highlights both achievements and persistent challenges particularly the overhead of physical qubits, the speed of real-time decoding, and integration into full-stack architectures. The analysis concludes that while scalable fault-tolerant quantum computing remains a work in progress, recent breakthroughs mark a decisive transition from abstraction to practicality, establishing QEC as a central pillar in the development of quantum computation, communication, and sensing.
This review article provides a comprehensive overview of recent developments in the field of quantum error correction (QEC), which stands as one of the biggest challenges for quantum computing. The extreme sensitivity of quantum systems to environmental noise makes it difficult to build reliable and scalable quantum computers. Inspired by pioneering codes like those from Shor and Steane, this work discusses the most promising QEC approaches today, particularly topological codes such as surface codes and low-density parity-check (LDPC) codes. The paper delves into critical experimental successes from industry leaders like Google, IBM, and Quantinuum, including their ”below-threshold” error correction demonstrations and roadmaps for fault-tolerant systems. It also presents a comparative analysis between classical algorithms like Minimum-Weight Perfect Matching (MWPM) and newer, machine learning-based decoder approaches. The discussion section addresses open problems that need to be solved in the future, such as correlated noise, cryogenic control, and the creation of fault-tolerant logical gate sets. This review aims to summarize the current state of the QEC field, serving as a guiding resource for both academics and industry professionals in shaping future research and development strategies.
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.