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Alexandria Engineering Journal

An efficient simulation of quantum error correction codes

R. Padma Priya, A. Baradeswaran

Published Jul 15, 2017• 7 citations
Publisher

Abstract

The QCAD which has been technologically advanced during last few years to support basic transformations, simulating multi-dimensional quantum devices and circuits. It is most important to demonstrate the theoretical operation of quantum computer using the simulator. Besides of describing various noise models in terms of quantum gates, a direct support of quantum error correction codes. Using the quantum error correction codes, the effects of applying single bit or phase flip error to the quantum circuits are reported along with the error recovery method for different qubit codes. The results are generated using the QCAD simulator. A simulation model for evaluating single qubit error in the proposed quantum circuit is also given. The working software prototype of an extremely efficient quantum computer simulator which is an attractive and versatile tool for both research and education.

DOI
10.1016/j.aej.2017.06.013

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The QCAD which has been technologically advanced during last few years to support basic transformations, simulating multi-dimensional quantum devices and circuits. It is most important to demonstrate the theoretical operation of quantum computer using the simulator. Besides of describing various noise models in terms of quantum gates, a direct support of quantum error correction codes. Using the quantum error correction codes, the effects of applying single bit or phase flip error to the quantum circuits are reported along with the error recovery method for different qubit codes. The results are generated using the QCAD simulator. A simulation model for evaluating single qubit error in the proposed quantum circuit is also given. The working software prototype of an extremely efficient quantum computer simulator which is an attractive and versatile tool for both research and education.
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Quantum technology is a new field of physics and engineering. In emerging areas like Quantum Cryptography, Quantum Computing etc, Quantum circuits play a key role. Quantum circuit is a model for Quantum computation, the computation process of Quantum gates are based on reversible logic. Encoder and Decoder are designed using Quantum gates, and synthesized in the QCAD simulator. Quantum error correction (QEC) is essential to protect quantum information from errors due to quantum noise and decoherence. It is also use to achieve fault-tolerant quantum computation that deals with noise on stored information, faulty quantum gates and faulty measurements.
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.
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.
Quantum noise cannot be avoided in the quantum computing devices due to unstable nature of qubits and signals. The error caused by quantum noise can be detected and corrected using different error correcting codes. In this work, we have tested the feasibility and accuracy of three qubit bit flip and phase flip error correcting code in quantum computer provided by International Business Machine Quantum Experience (IBM QX) cloud platform. Among five quantum processors, ibmq_ourense is found to have highest average accuracy 77.9% ± 3.09% on all qubits simultaneously. Three qubits bit flip error correction circuit gave correct output 89.9% ± 1.01% of the time on average. Similarly three qubits phase flip error correction circuit give 88.05% ±1.89%. The measurement error mitigation has improved the accuracy of bit flip and phase flip error correction code by 5.01% and 7.01% respectively on average. The error rate shows that the error in quantum computations are random in nature and can be corrected. IBM QX quantum computer are suitable for only small scale quantum computation and demonstrate purpose. Furthermore, the accuracy of error correction codes can be increased with the use of higher accuracy quantum qubits and quantum gates.
Recently, there has been a rapid increase in interest in quantum computers. Their work isbased on the use of quantum-mechanical phenomena such as superposition and entanglement forcomputing input data into output data that can actually provide effective performance 3 to 4 orders ofmagnitude higher than any modern computing devices, which will solve the above and others tasks ina natural and accelerated time scale. This article is devoted to solving the problem of research anddevelopment of corrective codes for correcting several types of quantum errors that appear duringcomputational processes in quantum algorithms and models of quantum computing devices. The aimof the work is to study existing methods for correcting various types and types of quantum errors andto create a 3-qubit corrective code for quantum error correction. The work touches upon the tasks ofresearch and development of the functioning methods of quantum circuits and models of quantumcomputing devices. The relevance of these studies lies in the mathematical and software modelingand implementation of corrective codes for correcting several types of quantum errors as part of thedevelopment and implementation of quantum algorithms for solving classes of classical problems.The scientific novelty of this area is expressed in the exclusion of one of the shortcomings of thequantum computing process. The scientific novelty of this area is primarily expressed in the constantupdating and addition of the field of quantum research in a number of areas, and computer simulation of quantum physical phenomena and features is poorly illuminated in the world. The aim of the work is computer simulation of a quantum computing process using the method of correctingphase types of errors, which allows one to evaluate the own phase of a unitary gate that hasgained access to the quantum state in proportion to its own vector.