Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly applicable form of capacity theorem for both classical and quantum information, i.e., hybrid information, with the assistance of a limited resource of entanglement in a one-shot scenario, which covers broader situations than the existing ones. Harnessing the wide applicability of the theorem, we show that a demonstration of QEC by short random quantum circuits is feasible and that QEC is intrinsic in quantum chaotic systems. Our results bridge the progress in quantum information theory, near-future quantum technology, and fundamental physics.
Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly applicable form of capacity theorem for both classical and quantum information, i.e., hybrid information, with the assistance of a limited resource of entanglement in a one-shot scenario, which covers broader situations than the existing ones. Harnessing the wide applicability of the theorem, we show that a demonstration of QEC by short random quantum circuits is feasible and that QEC is intrinsic in quantum chaotic systems. Our results bridge the progress in quantum information theory, near-future quantum technology, and fundamental physics.
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve fragile quantum states without copying them, measuring them directly, or destroying the information they encode. Driven by rapid progress in both theory and experiment, this challenge has grown into one of the most active areas of quantum information science. This tutorial gives a guided introduction to modern QEC, developing the core concepts of codes, syndromes, stabilizers, decoding, and fault tolerance before connecting them to major code families and current research directions. We cover both established constructions and newer developments, including topological and subsystem codes, bosonic and qudit codes, dynamical codes, and quantum low-density parity-check (qLDPC) codes. The emphasis is on building operational understanding: explaining not only what the main objects are, but how they are used in code design, error diagnosis, decoding, and fault-tolerant computation. The tutorial is intended for newcomers seeking a first path through QEC, as well as researchers looking for a coherent reference for the concepts, code families, and tools that arise in current work.
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.
In this thesis, we investigated a theory of quantum error correction (QEC) in nearterm quantum devices.Due to the recent development of quantum technologies, QEC with several tens of qubits is expected to be demonstrated in the next few years.On the other hand, since such a large quantum system cannot be tracked with current classical computers, several problems about practical QEC experiments emerge as quantum devices are scaled up.We provided solutions to the following two essential problems among them.First, we extended a simulatability of quantum error correcting code under coherent noise using matchgate circuits.This extension enables an efficient and accurate evaluation of an effective physical error probability suppressed with QEC under practical errors.Since this probability should be known before we design quantum devices for QEC, this result provides vital information for experiments.Second, we proposed a general framework to use machine learning as a part of decoding algorithm in QEC.QEC requires a fast and high-performance classical decoder for its implementation.Using machine learning for decoding is one of the most promising solutions to this.However, what part of a decoding algorithm should be delegated to machine learning in order to achieve the near-optimal performance has not been discussed.We constructed a general framework to discuss it, and showed fundamental relations between the decoding problem and the task of machine learning.Furthermore, we proposed a criterion for achieving high performance, and showed specific formulation of tasks of machine learning.Then, we confirmed that the performance of the proposed machine-learning-based decoder is superior to the known decoders in various situations.This thesis is written based on various supports and advice from many people.I would like to thank Prof. Masato Koashi, who has totally supervised my research during undergraduate and graduate school.His thoughtful advice and questions are helpful for me to obtain clear viewpoint of my research.I am frequently impressed by his outstanding perspective of quantum information science, and the discussions with him strongly encourage my interest in physics.I also would like to thank Assoc.Prof. Keisuke Fujii, who supervised both of the two main results of the thesis.My knowledge about quantum computation is supported by his deep understanding of it.I am very motivated by his strong enthusiasm for realizing quantum computer.Mr. Amarsanaa Davaasuren is a collaborator of the result about quantum error correction using machine learning discussed in Chapter 4 of this thesis.His many creative ideas about both machine learning and quantum information have amazed me.The result of Chapter 4 is largely supported by his collaboration.Assist.Prof. Takanori Sugiyama gave me lectures about the latest and essential problems in near-term quantum devices.In particular, his lectures were vital for us to find the research topic of an efficient simulation of quantum circuits of quantum error correction under practical noise models, which is discussed in Chapter 3 of this thesis.I have been financially supported by Advanced Leading Graduate Course for Photon Science (ALPS).During this program, I have had an opportunity to discuss with Prof. Akira Furusawa.His advice from the standpoint of an experimental researcher helps my practical understanding of experimental systems.His philosophy as a professional researcher shapes my attitude to research.I also would like to thank the members and alumni of Koashi's group.In particular, I thank Assoc.Prof. Haruka Tanji-Suzuki and Assist.Prof. Toshihiko Sasaki for advice about from fundamental physics to presentation skills.My skills as a researcher are trained through discussions with them.I also thank Dr. Yoshi
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.
Quantum error correction (QEC) is a critical requirement for reliable quantum computation, as errors can quickly accumulate and compromise the integrity of quantum states. Current QEC approaches often rely on encoding information redundantly across multiple qubits, which introduces significant overhead and complexity. This paper proposes a novel dimension expansion quantum error correction protocol (DEQ) that leverages the concept of dimensional expansion to enhance quantum information storage and transmission capabilities, ultimately improving the efficiency of error correction. We introduce a new strategy by strategically manipulating the quantum state to expand the system's dimensionality, allowing for more robust error detection and correction. This work explores the potential of this approach in mitigating the limitations of existing QEC methods and provides a foundational framework for future advancements in quantum information security.
Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspects of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large-scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large-scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. The development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.