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Chapman & Hall/CRC eBooks

Quantum Computation

Zijian Diao

Published Nov 2, 2006• 0 citations
Publisher

Abstract

Modern computer science emerged when the eminent British mathematician Alan Turing invented the concept of Turing machine (TM) in 1936. Though very simple and primitive, TM serves as the universal model for all known physical computation devices. The principles of quantum mechanics, another revolutionary scientific discovery of the 20 th century, had never been incorporated in the theory of computation until the early 1980s. P. Benioff first coined the concept of quantum Turing machine (QTM). Motivated by the problem that classical computers cannot simulate quantum systems efficiently, R. Feynman posed the quantum computer as the solution. The field of quantum computation was born.

DOI
10.1201/9781420010572-62

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Modern computer science emerged when the eminent British mathematician Alan Turing invented the concept of Turing machine (TM) in 1936. Though very simple and primitive, TM serves as the universal model for all known physical computation devices. The principles of quantum mechanics, another revolutionary scientific discovery of the 20 th century, had never been incorporated in the theory of computation until the early 1980s. P. Benioff first coined the concept of quantum Turing machine (QTM). Motivated by the problem that classical computers cannot simulate quantum systems efficiently, R. Feynman posed the quantum computer as the solution. The field of quantum computation was born.
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Universal computing can be dated to 1903 when Alan Turing’s theoretical model of the Turing machine led a large-scale innovative revolution towards digital computing machines.¹ The next milestone is to process and control information at its fundamental level — quantum states of particles. Richard Feynman first pointed out that as certain types of computational problems get more complex, classical bits fail to give efficient answers.² For example, when simulating quantum mechanics, the amount of memory needed to describe a quantum system increases exponentially with the number of its components. A new device — a quantum computer — is therefore highly sought after by physicists.³
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There is strong evidence that computers based upon the principles of quantum physics represent an inherently new and more powerful model of computation. Such computers violate the modern form of the Church-Turing thesis (which lies at the foundations of computer science). This thesis can be informally summarized as follows: all physical implementations of computing devices can be described by the same abstract model of computation-the probabilistic Turing Machine or the equivalent random access machine. In this paper, we will describe two formal models for quantum computers: quantum circuits and quantum Turing Machines, introduced by Deutsch [1985].