To use quantum information processing in a wide range of applications, fault-tolerant processing is essential to cope with noise.Fault-tolerant quantum computing using quantum error-correcting codes is scalable, but the overhead of number of qubits or processes is large, so improving efficiency is an important research theme.Quantum error mitigation incurs computational cost, but it does not require the overhead of number of qubits, so it is expected to be used for near-future applications.In this article, we introduce our research activities on these topics as well as our studies toward the implementation of quantum information processing.
To use quantum information processing in a wide range of applications, fault-tolerant processing is essential to cope with noise.Fault-tolerant quantum computing using quantum error-correcting codes is scalable, but the overhead of number of qubits or processes is large, so improving efficiency is an important research theme.Quantum error mitigation incurs computational cost, but it does not require the overhead of number of qubits, so it is expected to be used for near-future applications.In this article, we introduce our research activities on these topics as well as our studies toward the implementation of quantum information processing.
Quantum computers have the potential to solve several interesting problems in polynomial \ntime for which no polynomial time classical algorithms have been found. However, \none of the major challenges in building quantum devices is that quantum systems are very \nsensitive to noise arising from undesired interactions with the environment. Noise can lead \nto errors which can corrupt the results of the computation. Quantum error correction is \none way to mitigate the effects of noise arising in quantum devices. \nWith a plethora of quantum error correcting codes that can be used in various settings, \none of the main challenges of quantum error correction is understanding how well various \ncodes perform under more realistic noise models that can be observed in experiments. \nThis thesis proposes a new decoding algorithm which can optimize threshold values of \nerror correcting codes under different noise models. The algorithm can be applied to \nany Markovian noise model. Further, it is shown that for certain noise models, logical \nClifford corrections can further improve a code's threshold value if the code obeys certain \nsymmetries. \n \nSince gates and measurements cannot in general be performed with perfect precision, \nthe operations required to perform quantum error correction can introduce more errors \ninto the system thus negating the benefits of error correction. Fault-tolerant quantum \ncomputing is a way to perform quantum error correction with imperfect operations while \nretaining the ability to suppress errors as long as the noise is below a code's threshold. \nOne of the main challenges in performing fault-tolerant error correction is the high resource \nrequirements that are needed to obtain very low logical noise rates. With the use of \nflag qubits, this thesis develops new fault-tolerant error correction protocols that are applicable \nto arbitrary distance codes. Various code families are shown to satisfy the requirements \nof flag fault-tolerant error correction. We also provide circuits using a constant number of \nqubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewer \nqubits than previous fault-tolerant error correction protocols. \n \nIt is often the case that the noise afflicting a quantum device cannot be fully characterized. \nFurther, even with some knowledge of the noise, it can be very challenging to use \nanalytic decoding methods to improve the performance of a fault-tolerant scheme. This \nthesis presents decoding schemes using several state of the art machine learning techniques \nwith a focus on fault-tolerant quantum error correction in regimes that are relevant to near \nterm experiments. It is shown that even in low noise rate regimes and with no knowledge \nof the noise, noise can be further suppressed for small distance codes. Limitations of machine \nlearning decoders as well as the classical resources required to perform active error \ncorrection are discussed. \n \nIn many cases, gate times can be much shorter than typical measurement times of \nquantum states. Further, classical decoding of the syndrome information used in quantum \nerror correction to compute recovery operators can also be much slower than gate times. \nFor these reasons, schemes where error correction can be implemented in a frame (known \nas the Pauli frame) have been developed to avoid active error correction. In this thesis, we \ngeneralize previous Pauli frame schemes and show how Clifford frame error correction can \nbe implemented with minimal overhead. Clifford frame error correction is necessary if the \nlogical component of recovery operators were chosen from the Clifford group, but could \nalso be used in randomized benchmarking schemes.
A quantum computer is a powerful machine that provides a new approach to information processing based on quantum mechanics. However, basically, qubits are very vulnerable to errors, thus a quantum error correction code (QECC) is needed to build a reliable quantum computer. Moreover, simply using QECCs is not sufficient in order that a quantum computer can tolerate errors. In quantum computation, each operation must be performed on the encoded states. Even when the gates used to perform these operations are noisy, the quantum computation must be tolerable to the errors. This is called fault-tolerant quantum computation and it is an essential condition for implementing a quantum computer. However, considering the fault tolerance, the overhead of the quantum computer increases exponentially. In this paper, we introduce fault-tolerant quantum computation and schemes to reduce the its overhead.
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.
Fault-tolerant quantum computing (FTQC) is a form of universal quantum computing that suppresses physical errors via quantum error correction (QEC). On the other hand, it is expected that the available code distance and the T-gate count will be restricted in the early years of FTQC. Meanwhile, quantum error mitigation (QEM) was recently introduced for suppressing errors in noisy intermediate-scale quantum (NISQ) devices; it improves the computation accuracy of near-term quantum algorithms with its overhead being a greater number of samples. In this work, we integrate QEC and QEM into an efficient FTQC architecture that effectively increases the code distance and T-gate count. Our scheme will dramatically alleviate the required qubit count by tens of percent at the cost of a constant multiplicative sampling overhead within 102 in a wide range of regimes from the post-NISQ era to early FTQC regime, which necessitates the order of from 104 to 1010 logical operations. While it has been widely believed that there do not exist useful applications in post-NISQ regimes due to a chasm between the NISQ and FTQC regimes such as overheads for encoding and T-gate distillations, our scheme can continuously bridge the two distinct regimes.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.