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IEEE Access

Some Progress on Quantum Error Correction for Discrete and Continuous Error Models

Jincao Li

Published Jan 1, 2020• 1 citation
Publisher

Abstract

Quantum computing has increasingly gained attention for decades since it can surpass classical computing in various aspects. A crucial issue of quantum computing is how to protect information from noise interference such that the error rate during quantum information processing can be limited within an acceptable bound. The technique to address this issue is quantum error correction (QEC). Developing QEC technologies needs to define noise as formal error models and design QEC approaches for these error models. Discrete error models and continuous error models are two kinds of definitions of noise. The former assumes noise occurs independently and can be discretized into a set of basic errors. The former also has a tool, named quantum operations, to describe a specific error model. The latter describes that noise is continuous in time by using differential equations. In this paper, we categorize QEC approaches into three types according to the different error models: discrete error models, specific error models, and continuous error models. We also analyze the state-of-the-art QEC approaches and discuss some future directions. Furthermore, we propose the perturbed error models and their possible definitions, aiming to find the effect of the perturbation during quantum information processing.

DOI
10.1109/access.2020.2977344

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Quantum computing has increasingly gained attention for decades since it can surpass classical computing in various aspects. A crucial issue of quantum computing is how to protect information from noise interference such that the error rate during quantum information processing can be limited within an acceptable bound. The technique to address this issue is quantum error correction (QEC). Developing QEC technologies needs to define noise as formal error models and design QEC approaches for these error models. Discrete error models and continuous error models are two kinds of definitions of noise. The former assumes noise occurs independently and can be discretized into a set of basic errors. The former also has a tool, named quantum operations, to describe a specific error model. The latter describes that noise is continuous in time by using differential equations. In this paper, we categorize QEC approaches into three types according to the different error models: discrete error models, specific error models, and continuous error models. We also analyze the state-of-the-art QEC approaches and discuss some future directions. Furthermore, we propose the perturbed error models and their possible definitions, aiming to find the effect of the perturbation during quantum information processing.
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.
Quantum Error Correction (QEC) is an important technique for protecting quantum information against decoherence and errors. This involves the design and implementation of algorithms and techniques to minimize error rates and increase the stability of quantum circuits. One of the key parameters in QEC is the distance of the error- correcting code, which determines the number of errors that can be corrected. Another important parameter is the error probability, which quantifies the likelihood of errors occurring in the quantum system. In this context, the goal of a simulation sweeps like the one performed in the code is to study the performance of the QEC code for different values of the distance and error probability, and to optimize the code for maximum accuracy. By varying these parameters and observing the performance of the code, researchers can gain insights into how to design better codes and improve the reliability of quantum computing systems. We also discuss the challenges that need to be addressed for quantum computing to realize its potential in solving practical Error-correction problems.
Quantum Error Correction (QEC) is the process of detecting and correcting errors in quantum systems, which are prone to decoherence and quantum noise. QEC is crucial for developing stable and highly accurate quantum computing systems, therefore, several research efforts have been made to develop the best QEC strategy. Recently, Google's breakthrough shows great potential to improve the accuracy of the existing error correction methods. This survey provides a comprehensive review of advancements in the use of artificial intelligence (AI) tools to enhance QEC schemes for existing Noisy Intermediate Scale Quantum (NISQ) systems. Specifically, we focus on machine learning (ML) strategies and span from unsupervised, supervised, semi-supervised, to reinforcement learning methods. It is clear from the evidence, that these methods have recently shown superior efficiency and accuracy in the QEC pipeline compared to conventional approaches. Our review covers more than 150 relevant studies, offering a comprehensive overview of progress and perspective in this field. We organized the reviewed literature on the basis of the AI strategies employed and improvements in error correction performance. We also discuss challenges ahead such as data sparsity caused by limited quantum error datasets and scalability issues as the number of quantum bits (qubits) in quantum systems kept increasing very fast. We conclude the paper with summary of existing works and future research directions aimed at deeper integration of AI techniques into QEC strategies.
Quantum Error Correction (QEC) is an important technique for protecting quantum information against decoherence and errors. This involves the design and implementation of algorithms and techniques to minimize error rates and increase the stability of quantum circuits. One of the key parameters in QEC is the distance of the error- correcting code, which determines the number of errors that can be corrected. Another important parameter is the error probability, which quantifies the likelihood of errors occurring in the quantum system. In this context, the goal of a simulation sweep like the one performed in the code is to study the performance of the QEC code for different values of the distance and error probability, and to optimize the code for maximum accuracy. By varying these parameters and observing the performance of the code, researchers can gain insights into how to design better codes and improve the reliability of quantum computing systems. We also discuss the challenges that need to be addressed for quantum computing to realize its potential in solving practical Error-correction problems.
We present a discussion of the continuous-time quantum error correction introduced by J. P. Paz and W. H. Zurek [Proc. R. Soc. A 454, 355 (1998)]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the three-qubit and five-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame features a short initial transient in which error correction is ineffective, followed by a slow decay of the information content consistent with the known facts about discrete-time error correction in the limit of fast operations. This behavior is explained in the two case studies through a geometric description of the continuous transformation of the state space induced by the combined action of noise and error correction.
Canonical discrete quantum error correction (DQEC) schemes use projective von Neumann measurements on stabilizers to discretize the error syndromes into a finite set, and fast unitary gates are applied to recover the corrupted information. Quantum error correction (QEC) based on continuous measurement, known as continuous quantum error correction (CQEC), in principle, can be executed faster than DQEC and can also be resource efficient. However, CQEC requires meticulous filtering of noisy continuous measurement data to reliably extract error syndromes on the basis of which errors could be detected. In this paper, we show that by constructing a measurement-based estimator (MBE) of the logical qubit to be protected, which is driven by the noisy continuous measurement currents of the stabilizers, it is possible to accurately track the errors occurring on the physical qubits in real time. We use this MBE to develop a continuous quantum error correction (MBE-CQEC) scheme that can protect the logical qubit to a high degree, surpassing the performance of DQEC, and also allows QEC to be conducted either immediately or in delayed time with instantaneous feedbacks.