Quantum computer performs operations by adopting the principles of quantum physics and quantum mechanics. With these principles, it performs operations exponentially faster compared to classical computers. The major problem observed in quantum computation is noise and decoherence. The noise and decoherence generate errors while performing the operations on quantum states. As a solution to this Quantum error correction(QEC) methods are introduced. Encoding plays a key role in QEC. In the encoding process, the logical qubits are encoded into physical qubits by appending extra qubits to them. With this, the logical qubit will be strengthened and can be transferred safely. Initially, the experimental results of quantum computation are theoretical or mathematical. But with the existence of quantum computers, it is possible to develop and run new quantum architectures on publicly available quantum computers. Thus in this paper, we developed an efficient algorithm for encoding quantum information using various quantum gates. The developed algorithm is executed on various quantum systems and the performance is analyzed in terms of frequency, run time, error rate, number of qubits, and quantum volume. This analysis helps the researchers to opt an efficient quantum system to perform the experiments.
Quantum computer performs operations by adopting the principles of quantum physics and quantum mechanics. With these principles, it performs operations exponentially faster compared to classical computers. The major problem observed in quantum computation is noise and decoherence. The noise and decoherence generate errors while performing the operations on quantum states. As a solution to this Quantum error correction(QEC) methods are introduced. Encoding plays a key role in QEC. In the encoding process, the logical qubits are encoded into physical qubits by appending extra qubits to them. With this, the logical qubit will be strengthened and can be transferred safely. Initially, the experimental results of quantum computation are theoretical or mathematical. But with the existence of quantum computers, it is possible to develop and run new quantum architectures on publicly available quantum computers. Thus in this paper, we developed an efficient algorithm for encoding quantum information using various quantum gates. The developed algorithm is executed on various quantum systems and the performance is analyzed in terms of frequency, run time, error rate, number of qubits, and quantum volume. This analysis helps the researchers to opt an efficient quantum system to perform the experiments.
Quantum error correction (QEC) is required in quantum computers to mitigate the impact of errorson physical qubits. The goal is to optimize the neural network for high decoding performance whilemaintaining a minimalistic hardware implementation. The errors associated with decoherence can bereduced by adopting QEC schemes that encode multiple imperfect physical qubits into a logical quantumstate, similar to classical error correction. The relevance of these studies lies in the mathematicaland software modeling and implementation of corrective codes to correct several types of quantumerrors in the development and implementation of quantum algorithms for solving classes of problems ofa classical nature. The scientific novelty of this direction is expressed in the elimination of one of theshortcomings of the quantum computing process. The development of the theory and principles for constructingmodeling systems that are resistant to external interference (dependence of data distortion onnoise, dependence of the error of a quantum computing process on the measure and purity of entanglement)for modeling quantum computing is a dynamic area, as evidenced by a large number of existingmodels reflecting certain quantum computational processes and phenomena (quantum teleportation,parallelism, entanglement of quantum states) and scientific papers. Although quantum computing is notyet ready to move from theory to practice, it is nevertheless possible to reasonably guess what form aquantum computer might take, or, more importantly for programming language design, what interface itwould be possible to interact with such a quantum computer. It is natural to apply the lessons learnedfrom the programming of classical computing to quantum computing. The analysis of works in this areashowed that a new qualitative level has now been reached, which opens up promising opportunities forthe implementation of multi-qubit quantum computing. Prospects for implementation and developmentare associated not only with technological capabilities, but also with the solution of issues of buildingeffective quantum systems for solving actual mathematical problems, cryptography problems and control(optimization) problems.
Quantum error correction plays a vital role in the Quantum information process. Nowadays, the research has been increased in quantum technology and is being applied in various applications like secure communications, finance, machine learning, drug analysis and etc. But the quantum information process is difficult compared to the classical due to the challenges in quantum technology like no-cloning theorem, decoherence, and the difficulty in quantum states measurement. Thus the error rate is high and it is not possible to build a quantum computer without an error detection and correction mechanism. In this paper, we are discussing various error correction methods and proposing a novel encoding method for quantum error correction.
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses these measurements to infer which error most likely occurred, so that the system can correct it. The decoder's accuracy-how rarely it makes the wrong guess-directly determines the scale of quantum computation that can be reliably executed. With a wealth of competing decoding algorithms, a QEC system designer needs reliable methods to evaluate them. Today, the dominant approach is to evaluate decoders using Monte Carlo simulation. However, simulation has several drawbacks such as requiring many samples to produce low variance estimates.
In this work, we develop a new systematic analysis for evaluating decoders. We introduce a novel formal semantics of a core language for QEC programs that captures the de facto standard Stim circuit format, providing a principled theoretical foundation for the emerging space of fault-tolerant quantum systems design. Given a QEC program and a decoder, our verifier can quantify both the decoder accuracy and the decoder robustness to drift in physical error rate. Our approach has two key components: (i) a structured search over the space of possible errors; and (ii) a constrained polynomial optimization kernel. A thorough empirical evaluation of our approach suggests that it can outperform simulation, especially in low error rate regimes, and that it can be deployed to quantify decoder robustness over an interval of physical error rates.
In recent years, interest in quantum computers has grown significantly. While commercial quantum computers are not available yet, both private and public sector investment into developing quantum computers has developed considerably. One of the key challenges in quantum computing is optimizing the performance of the quantum hardware devices. Different factors can be put into consideration regarding this point, including the number of gates used by the processors to execute different quantum computations and operations. This paper focuses on developing quantum hardware metrics that can be used to measure the performance of a quantum processor in terms of number of quantum gates needed to execute different quantum algorithms. The proposed metrics have been implemented and experimental evaluations have been conducted on various IBM back-end Quantum Computers and using 4 different algorithms: a 5-Qubit entangled circuit algorithm, a 5-Qubit implementation of Grover’s quantum search algorithm, a 5-Qubit implementation of Simon’s quantum algorithm and the 7-Qubit implementation of Steane’s error correction quantum algorithm. In addition, quantitative data on the number of quantum gates used by quantum processors to execute the different quantum algorithms were gathered, which enabled the analysis of how the availability and compatibility of different gate sets affect the overall number of quantum gates needed in the execution of the different quantum algorithms.
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 computing exists at the intersection of mathematics, physics, chemistry, and engineering; the main goal of quantum computing is the creation of devices and algorithms which use the properties of quantum mechanics to store, manipulate and measure information. There exist many families of algorithms, which, using non-classical logical operations, can outperform traditional, classical algorithms in terms of memory and processing requirements. In addition, quantum computing devices are fundamentally smaller than classical processors and memory elements; since the physical models governing their performance are applicable on all scales, as opposed to classical logic elements, whose underlying principles rely on the macroscopic nature of the device in question. \n \nQuantum algorithms, for the most part, are predicated on a theory of resources. It is often assumed that quantum computers can be placed in a precise fiducial state prior to computation, and that logical operations are perfect, inducing no error on the system which they affect. These assumptions greatly simplify algorithmic design, but are fundamentally unrealistic. In order to justify their use, it is necessary to develop a framework for using a large number of imperfect devices to simulate the action of a perfect device, with some acceptable probability of failure. This is the study of fault-tolerant quantum computing. In order to pursue this study effectively, it is necessary to understand the fundamental nature of generic quantum states and operations, as well as the means by which one can correct quantum errors. Additionally, it is important to attempt to minimize the use of computational resources in achieving error reduction and fault-tolerant computing. \n \nThis thesis is concerned with three projects related to the use of error-prone quantum systems to transmit and manipulate information. The first of these is concerned with the use of imperfectly-prepared states in error-correction routines. Using optimal quantum error correction, we are able to deduce a method of partially protecting encoded quantum information against preparation errors prior to encoding, using no additional qubits. The second of these projects details the search for entangled states which can be used to transmit classical information over quantum channels at a rate superior to classical states. The third of these projects concerns the transcoding of data from one quantum code into another using few ancillary resources. The descriptions of these projects are preceded by a brief introduction to representations of quantum states and channels, for completeness. \n \nThree techniques of general interest are presented in appendices. The first is an introduction to, and a minor advance in the development of optimal error correction codes. The second is a more efficient means of calculating the action of a quantum channel on a given state, given that the channel acts non-trivially only on a subsystem, rather than the entire system. Finally, we include documentation on a software package developed to aid the search for quantum transcoding operations.