In recent years, quantum information systems have attracted increasing attention of researchers in the field of computer science and physics. However, the introduction and practical application of quantum computing is limited by the influence of noise and errors that occur in quantum systems. To implement effective control and improve the reliability of quantum information systems, it is necessary to develop methods that can suppress and correct errors in the process of quantum computing. The purpose of this work is to develop and study a control model based on noise-immune quantum computing, as well as methods for suppressing and correcting errors in quantum computing. The paper proposes a combination of different approaches, including the use of error correction codes, noise suppression algorithms, and methods for optimal control of quantum information systems. In the course of the study, a control model was developed that allows efficient processing of information in quantum systems, taking into account the presence of noise and errors. Experiments were carried out using real quantum devices to evaluate the effectiveness of the proposed model. The experimental results show that the developed method can significantly improve the reliability and accuracy of quantum computing. The proposed control model based on noise-immune quantum computing and methods for suppressing and correcting errors represent a significant contribution to the development of quantum information systems. Further development and optimization of the proposed approach can lead to the creation of more reliable and efficient quantum systems capable of solving complex computational problems.
In recent years, quantum information systems have attracted increasing attention of researchers in the field of computer science and physics. However, the introduction and practical application of quantum computing is limited by the influence of noise and errors that occur in quantum systems. To implement effective control and improve the reliability of quantum information systems, it is necessary to develop methods that can suppress and correct errors in the process of quantum computing. The purpose of this work is to develop and study a control model based on noise-immune quantum computing, as well as methods for suppressing and correcting errors in quantum computing. The paper proposes a combination of different approaches, including the use of error correction codes, noise suppression algorithms, and methods for optimal control of quantum information systems. In the course of the study, a control model was developed that allows efficient processing of information in quantum systems, taking into account the presence of noise and errors. Experiments were carried out using real quantum devices to evaluate the effectiveness of the proposed model. The experimental results show that the developed method can significantly improve the reliability and accuracy of quantum computing. The proposed control model based on noise-immune quantum computing and methods for suppressing and correcting errors represent a significant contribution to the development of quantum information systems. Further development and optimization of the proposed approach can lead to the creation of more reliable and efficient quantum systems capable of solving complex computational problems.
In recent years, quantum information systems have attracted increasing attention of researchersin the field of computer science and physics. However, the introduction and practicalapplication of quantum computing is limited by the influence of noise and errors that occur inquantum systems. To implement effective control and improve the reliability of quantum informationsystems, it is necessary to develop methods that can suppress and correct errors in theprocess of quantum computing. The purpose of this work is to develop and study a control modelbased on noise-immune quantum computing, as well as methods for suppressing and correctingerrors in quantum computing. The paper proposes a combination of different approaches, includingthe use of error correction codes, noise suppression algorithms, and methods for optimal controlof quantum information systems. In the course of the study, a control model was developedthat allows efficient processing of information in quantum systems, taking into account the presenceof noise and errors. Experiments were carried out using real quantum devices to evaluate theeffectiveness of the proposed model. The experimental results show that the developed method cansignificantly improve the reliability and accuracy of quantum computing. The proposed controlmodel based on noise-immune quantum computing and methods for suppressing and correctingerrors represent a significant contribution to the development of quantum information systems.Further development and optimization of the proposed approach can lead to the creation of morereliable and efficient quantum systems capable of solving complex computational problems.
Abstract Intensive research is currently being carried out to develop and create quantum computers and their software. This work is devoted to study of the influence of the environment on the quantum system of qubits. Quantum error correction is a set of methods for protecting quantum information and quantum state from unwanted interactions of the environment (decoherence) and other forms and types of noise. The article discusses the solution to the problem of research and development of corrective codes for rectifying several types of quantum errors that occur during computational processes in quantum algorithms and models of quantum computing devices. The aim of the work is to study existing methods for correcting various types of quantum errors and to create a corrective code for quantum error rectification. The scientific novelty is expressed in the exclusion of one of the shortcomings of the quantum computing process.
Quantum computing holds immense promise for revolutionizing various fields, but its inherent susceptibility to noise poses a significant challenge to achieving reliable computations. This work investigates the degradation of quantum information due to noise and proposes an optimized approach to error-correcting codes specifically tailored for quantum systems. We establish a precise noise degradation model, incorporating various noise types and their statistical properties, represented as (σi). This model allows for a more realistic simulation of quantum noise compared to traditional approaches. Subsequently, we employ an optimization algorithm, based on the principle of minimizing bit-flip error rates, to design error-correcting codes. The core of our design strategy leverages information theory concepts, particularly channel capacity and mutual information, represented as (Cch, Imn), to determine the optimal code parameters. The optimization process aims to find the most efficient code that can effectively protect quantum information from noise, ultimately enhancing the reliability of quantum computations. The final optimized code is characterized by its encoding rate (R), decoding rate (D), and the minimum distance (dmin) of the code, represented as (R, D, dmin). The results demonstrate the effectiveness of our approach in mitigating noise degradation and improving the performance of quantum error correction.
This work is a study of the influence of the medium on the quantum system of qubits. The article assumes a description of the fundamentals of the quantum information theory, as well as a place in it the concept of quantum entanglement. Quantum error correction is a set of methods for protecting quantum information and quantum state from unwanted interactions of the environment (decoherence) and other forms and types of noise. Today, there are modern quantum technologies that are capable of supporting fundamentally new computational algorithms based on the principles of quantum mechanics. The dependences of data distortion on noise and measures of decoherence on noise in one qubit are demonstrated. This article is devoted to solving the problem of research and development of corrective codes for correcting several types of quantum errors. These errors appear during computational processes in quantum algorithms and models of quantum computing devices. The aim of the work is to study existing methods for correcting various types of quantum errors and to create a corrective code for quantum error correction. The scientific novelty of this research is expressed in the one shortcoming exclusion of the quantum computing process. Currently, in many advanced countries of the world, intensive research is being carried out to develop and create quantum computers and their software, and there has been a rapid increase in interest in quantum computers. A large number of articles and monographs are published.
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 mathematical model of computation is an idealized abstraction. We design algorithms and perform analysis on the assumption that the mathematical operations we specify will be carried out exactly, and without error. Physical devices that implement an abstract model of computation are imperfect and of limited precision. For example, when a digital circuit is implemented on a physical circuit board, unwanted electrical noise in the environment may cause components to behave differently than expected, and may cause voltage levels (bit-values) to change. These sources of error must be controlled or compensated for, or else the resulting loss of efficiency may reduce the power of the information-processing device. If individual steps in a computation succeed with probability p, then a computation involving t sequential steps will have a success probability that decreases exponentially as pt. Although it may be impossible to eliminate the sources of errors, we can devise schemes to allow us to recover from errors using a reasonable amount of additional resources. Many classical digital computing devices use error-correcting codes to perform detection of and recovery from errors. The theory of error-correcting codes is itself a mathematical abstraction, but it is one that explicitly accounts for errors introduced by the imperfection and imprecision of realistic devices. This theory has proven extremely effective in allowing engineers to build computing devices that are resilient against errors. Quantum computers are more susceptible to errors than classical digital computers, because quantum mechanical systems are more delicate and more difficult to control. If large-scale quantum computers are to be possible, a theory of quantum error correction is needed. The discovery of quantum error correction has given researchers confidence that realistic large-scale quantum computing devices can be built despite the presence of errors. We begin by considering fundamental concepts for error correction in a classical setting. We will focus on three of these concepts: (a) the characterization of the error model, (b) the introduction of redundancy through encoding, and (c) an error recovery procedure. We will later see that these concepts generalize quite naturally for quantum error correction.