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Physics World

Decoherence: the obstacle to quantum computation

David Peter Divincenzo, Barbara M. Terhal

Published Mar 1, 1998• 35 citations
Publisher

Abstract

Alan Turing laid the foundation for the modern computer in 1936 when he introduced the concept of a universal computer; now known as a Turing machine. But it took another 10 years of research before the first electronic computer, the ENIAC, was actually built by scientists at the University of Pennsylvania. The ENIAC was capable of performing arithmetic on numbers Up to 10 digits long.

DOI
10.1088/2058-7058/11/3/32

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Alan Turing laid the foundation for the modern computer in 1936 when he introduced the concept of a universal computer; now known as a Turing machine. But it took another 10 years of research before the first electronic computer, the ENIAC, was actually built by scientists at the University of Pennsylvania. The ENIAC was capable of performing arithmetic on numbers Up to 10 digits long.
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.
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
It took only 40 years from the first ideas about using quantum physics as a basis for computing to the first working computers and the topic is gaining speed. Progress in quantum computer hardware development is accelerating significantly. When scientists started keeping a single qubit alive some 20 years ago, they struggled manipulating it in any useful manner. We now not only have quantum computers with hundreds and even over a thousand of qubits available, but they also provide a set of universal logical gates. This chapter lays the foundation to understand the mathematics behind this fascinating development by investigating the fundamental principles of quantum computing and quantum communications. We introduce the basic concepts like superposition, entanglement, and qubits.
In the twentieth century, quantum physics is one of the most successful approaches in scientific progress. To theorize the concept of quantum computing Max Planck's idea of the existence of energy in individual units like matter was used. Since then, the idea of manufacturing quantum computers for everyday use is becoming more plausible with technological advances in quantum theory. A classical computer carries out logical operations using a bit which is either 1 or 0. In contrast to a classical computer, a quantum computer works with a quantum bit or qubit, which is not limited to two states only. Qubits can exist in a superposition of the two states creating parallelism. Qubit represents the state of atoms, ions, photons or electrons. These qubits which work together with a control device act as a computer memory.Quantum computers have the potential to become million times more potent than present-day supercomputers due to the presence of these multiple states simultaneously. Concepts and ideas of quantum computing have been demonstrated by different methods like Ion Trap, Quantum Dot methods etc. However, the actual realization of such a superior system is still in the future. A strategy must be formulated to maintain decoherence and other potential sources of error at a permissible level.Astonishingly, quantum computing took a long time to take off, even though the physicists have known about the world of subatomic particles. Even so, it took computer scientists another half-century to consider harnessing quantum effects for computation. Also, it was later discovered that quantum computers could solve quantum mechanical many-body problems that are impractical to solve on a classical computer. The foundations of the subject of quantum computation may have become well-published, but the knowledge is still growing. Hence here is a research paper based on the study of quantum computation.
The idea of using quantum mechanics to provide more power than classical computers seem to have begun around 1981 to 1982, but Deutsch put the concept on a sounder footing a short time later. Deutsch reformulated the Turing thesis with the assertion that every finite realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means. However, he asserted that the output of a quantum machine, although fully determined by the input state, is not an observable itself. Progress beyond mathematical approaches came later when Lloyd suggested that arrays of weakly coupled quantum systems might be able to serve as the quantum computer if they were subjected to a sequence of controlled electromagnetic pulses, which could place the quantum bits into the desired super-positions. It was John von Neumann, working with the computer pioneers at the University of Pennsylvania, who suggested that the binary system should be used for simplicity in building computers.