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International Journal of Advanced Trends in Computer Science and Engineering

A Novel Framework for Simulation of Quantum Information System

Binh A. Nguyen

Published Apr 25, 2020• 4 citations
Publisher

Abstract

Nowadays, quantum computers have been proven to solve the complex problem more efficient and process data more security than classical computer.However, the effect of noises and unwanted environments make the needs of quantum error correction code to build the practical quantum information system.Since the quantum computation algorithms need to be verified in classical computer before implement in quantum computers, the novel framework for verification in classical computer has been become essentially and importantly.In this discussion, a novel framework for quantum information system simulation is proposed which is based on MATLAB environment.First, we analysis the basic notation and elementary elements of a quantum system via mathematical model.Then, we introduce the basic elements of Pauli channel model, and two basic quantum error correction codes to stabilize the quantum channel.Hence, the proposed system to simulate the quantum three-repetition codes and quantum Shor codes are discussed.

DOI
10.30534/ijatcse/2020/129922020

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Recently, Samsung Electronic just released a new type of mobile phone model named Galaxy A71 where the quantum RNG chip is boasted inside for advanced security by capable of generating truly random and unpredictable numbers.It is no doubt that the quantum mechanism-based communication protocols or quantum information technologies are gradually changing the world with its advantages.It promises the new information generation where quantum-based computer can be seen in many living fields.Since the quantum algorithms and quantum communication protocols need to be verified before applying on chip set system, or hardware systems, the verification frameworks need to be done.In this discussion, we first propose a novel framework by MATLAB emulators.Then, we analysis the quantum resources or quantum basic elements such as quantum entanglements, quantum super positions state, quantum Fourier transformation, and quantum Arithmetic in proposed novel framework.The open problems to consider quantum algorithms based on proposed framework is discussed.
Quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. Moreover, quantum channel models that are efficiently implementable and manageable on classical computers are required in order to design and simulate such error correction schemes. In this article, we present a survey of decoherence models, reviewing the manner in which these models can be approximated into quantum Pauli channel models, which can be efficiently implemented on classical computers. We also explain how certain families of quantum error correction codes can be entirely simulated in the classical domain, without the explicit need of a quantum computer. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte Carlo simulations on a classical computer.
Quantum computing is a computer development technology that uses quantum mechanics to perform the operations of data and information. It is an advanced technology, yet the quantum channel is used to transmit the quantum information which is sensitive to the environment interaction. Quantum error correction is a hybrid between quantum mechanics and the classical theory of error-correcting codes that are concerned with the fundamental problem of communication, and/or information storage, in the presence of noise. The interruption made by the interaction makes transmission error during the quantum channel qubit. Hence, a quantum error correction code is needed to protect the qubit from errors that can be caused by decoherence and other quantum noise. In this paper, the digital system design of the quantum error correction code is discussed. Three designs used qubit codes, and nine-qubit codes were explained. The systems were designed and configured for encoding and decoding nine-qubit error correction codes. For comparison, a modified circuit is also designed by adding Hadamard gates.
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
Classical simulations of quantum computers give us an insight into various things such as what quantum algorithms can achieve, whether it is possible to verify that they function as postulated, the difficulties that have to be overcome before quantum computers can be realized, as well as how we can handle these difficulties. We build a Python library to simulate a quantum computer that can perform all quantum algorithms by defining an universal gate set, from which all quantum gates – and thereby all circuits – can be constructed. We implement two algorithms that both highlight two important aspects of quantum computing: Grover’s quantum search algorithm, which demonstrates the efficiency of quantum algorithms and their superiority over their classical counterparts by searching an unsorted list quadratically faster; and an error correcting code, the Shor code, which highlights the cost of correcting the possible errors in a quantum computer.We test the rigidity of Grover’s algorithm by introducing errors without correction, and find that the algorithm shows resilience to smaller 1-qubit Pauli errors, but looses its efficiency under larger errors and thus the need for Pauli error correction arise.