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
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 computers have the potential to solve certain problems exponentially faster than classical computers. However, realizing this potential in practice is a major challenge, as it requires precise control over large-scale quantum systems operating at extremely low error rates. Quantum error correction (QEC) provides a path to achieving such error rates, but its substantial resource overhead poses a significant practical barrier. In addition, identifying which computational problems offer a provable quantum advantage—and which remain fundamentally intractable—remains an open question. This thesis presents progress towards addressing both of these challenges. The first part of this thesis describes advances that substantially reduce the resource overhead of QEC. We begin by presenting realizations of logical circuits in dynamically reconfigurable arrays of neutral atoms. By jointly decoding the logical qubits, we reduce the cost of implementing such transversal Clifford circuits by a factor proportional to the code distance. We then develop new theories of fault tolerance to extend these savings to universal quantum computation with magic state inputs. Finally, we introduce techniques for fast correlated decoding, enabling practical implementations of these improvements in experimental hardware. Collectively, these advances accelerate progress toward large-scale computation and reduce the cost of QEC by over an order of magnitude. The second part of the thesis explores the relative power of quantum and classical computation in combinatorial optimization, a class of problems that is ubiquitous in science and engineering and foundational to the theory of computational complexity. We experimentally implement the optimized quantum adiabatic algorithm (QAA) in neutral atom arrays and observe evidence of a superlinear speedup over classical simulated annealing on certain hard problem instances. To interpret these results, we develop a theoretical framework to compare the performance of QAA with a broad class of classical Markov chain Monte Carlo algorithms. We identify conditions under which a quantum quadratic speedup is achievable and propose modifications to the QAA to reliably realize this advantage. Together, these contributions advance both the practical implementation and theoretical understanding of quantum algorithms.
Quantum computation is expected to have significant practical applications. The main problem in quantum computing is susceptibility to noise. Quantum error correction was developed to allow large-scale applications of quantum computing by achieving fault tolerance. However, as large-scale fault-tolerant quantum computation is not available, the question of applications of near-term hardware remains important. Current noisy intermediate-scale (NISQ) quantum devices can be used for small applications or as testbeds for larger applications; noise suppression techniques are of significant importance to their applicability. This thesis addresses noise suppression via quantum error mitigation (QEM) and quantum error correction (QEC) for near-term applications. The work aims to improve the understanding of noise-suppression techniques and their performance for exploring the physical systems of interest. The results presented in this thesis are divided into QEM and QEC chapters. The majority of the work is focused on QEM. The main interest of this thesis is the application of QEM to Hamiltonian simulations. Two simulation methods: the Trotter method and a quantum signal processing-based method, are explored. Both simulation methods, enhanced by zero-noise extrapolation, are employed to simulate the transverse-field Ising model. The obtained numerical results are promising, as the QEM allows a good recovery of noiseless values in low-noise shallow circuits, even with fixed sampling resources. A further result obtained in the QEM domain is a definition of a mitigation technique based on optimal measurement (in a metrological sense). The presentation includes analytical calculations of implementation costs and error propagation, as well as a numerical application to Hamiltonian simulation, yielding promising results: noise suppression by several orders of magnitude. The QEC part of the thesis explores its application in quantum metrology. The focus is on parameter sensing in many-body Hamiltonians. The results are purely analytical and extend a known lemma to m-local homogeneous Pauli Hamiltonian parameter sensing. This allows discussion of the scaling achieved for sensing the Hamiltonian parameters with respect to the code properties. The results in this thesis establish applications of QEM and QEC in selected near-term applications, quantify their performance, and discuss caveats and potential future applications. This thesis presents a theoretical and numerical study with implications for future experimental implementations. The relative success of the QEM and QEC shown in this thesis relies on tailoring the techniques to a chosen problem, highlighting the importance of technique adaptation in near-term applications.
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 computation has the promise to solve problems that are not efficiently solvable by classical means. Yet, due to the fragile nature of quantum states, it is unavoidable that quantum systems are subject to decoherence, gate imperfections, and measurement errors. These problems stand as a major roadblock to the construction of large-scale fault-tolerant quantum computers. Conventional quantum error correction (QEC) codes, such as the surface code or Shor code, need to use an extensive amount of redundancy and classical control, which can be both computationally expensive and challenging to scale. In this context, we propose to investigate the use of machine learning (ML) techniques by realizing on-line identification, localization and correction of these quantum errors for fault-tolerant quantum computation by means of fault-tolerant quantum computing processes. Our model introduces a hybrids ML-QEC architecture that combines classical neural networks and decision-tree classifiers with quantum syndrome decoding. These models are trained on error syndromes produced using the approximation of common noise models (for example, depolarizing noise, dephasing and amplitude damping), simulated under different QEC schemes. The machine learning methods are trained with quantum error patterns and have a capability to rapidly infer where errors are likely to occur, as well as recommend correction operations with high confidence. As a result, the system reduces dramatically the delay and computational costs when compared to conventional decoding methods. There is also a self-adaptive learning module in the work, which recommences training on fresh quantum error distributions, meaning the system can adapt to changes in the environment (and also the decay of the hardware) as time progresses. The study further carries out ML predictions inside a real-time loop and cross-checks them with quantum state tomography and entanglement fidelity such as indicators. Experimental characterization on dedicated devices as well as noise models show that our ML-enhanced decoders reach higher fidelity and lower logical error rates compared to baseline decoders, especially in non-uniform or time-dependent noise. This work is a significant stride towards realizing practical fault-tolerant quantum computation by combining quantum error correction with the versatility and scalability of machine learning. With intelligent models to dictate learning, our proposed framework is able to eliminate a lot of trial-and-error manual processes in the conventional heuristic-based approach, and points to a potential path to achieve scalable quantum information processing platforms.
The development of quantum computers requires not only experimental advances, but also theoretical efforts to tackle the bottlenecks and identify potential applications. This thesis addresses some essential elements in each stage of the development of quantum computers, from the currently available hardware to the long-term devices. The critical factor that hinders the quantum hardware from performing perfect operations is the presence of noise, however, it can be overcome by error correction codes. We first consider a large-scale quantum processor with asymmetrical noise and preferably a modular structure. By concatenating the surface code with an error-detecting code, and utilising the information from detection with a customised decoder, we find very high thresholds for the designed devices. The second topic is small error correction codes which are more realistic to be implemented in the near future. A measure `integrity' is introduced to benchmark the performance of quantum memories to demonstrate beneficial error correction, associated with four milestones. We show integrity is closely related with other commonly-used measures and can be easily assessed by experimentalists. This framework is then studied in detail in the context of an ion-trap quantum device implemented with the seven qubit code. We present a protocol based on detailed sequences of crystal-reconfiguration operations and stabiliser mappings to perform a full error correction cycle. Realistic error models and parameters from reported works are also given. While experimental efforts continue to battle against the noise, some hybrid quantum-classical algorithms have been developed to be implemented on the near-term noisy devices. The variational algorithm is one of the hybrid algorithms that have been widely applied to simulations of condensed matter physics and quantum chemistry. In the next chapter, we introduce a variational quantum compiler to automatically search for the encoding circuits of small error correction codes. By tailoring the ansatz to optimise the circuit for particular hardware systems, we show some novel circuits discovered with the compiler. The final chapter applies the variational algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications. We show that the linear algebra problems can be solved with near-term devices, with circuit depth linear to the condition number and super-linear to the number of qubits.