Quantum Physics and Information Processing: Quantum Computers

Phillip Kaye, Raymond Laflamme, Michele Mosca

A computer is a physical device that helps us process information by executing algorithms. An algorithm is a well-defined procedure, with finite description, for realizing an information-processing task. An information-processing task can always be translated into a physical task. When designing complex algorithms and protocols for various information-processing tasks, it is very helpful, perhaps essential, to work with some idealized computing model. However, when studying the true limitations of a computing device, especially for some practical reason, it is important not to forget the relationship between computing and physics. Real computing devices are embodied in a larger and often richer physical reality than is represented by the idealized computing model. Quantum information processing is the result of using the physical reality that quantum theory tells us about for the purposes of performing tasks that were previously thought impossible or infeasible. Devices that perform quantum information processing are known as quantum computers. In this book we examine how quantum computers can be used to solve certain problems more efficiently than can be done with classical computers, and also how this can be done reliably even when there is a possibility for errors to occur. In this first chapter we present some fundamental notions of computation theory and quantum physics that will form the basis for much of what follows. After this brief introduction, we will review the necessary tools from linear algebra in Chapter 2, and detail the framework of quantum mechanics, as relevant to our model of quantum computation, in Chapter 3. In the remainder of the book we examine quantum teleportation, quantum algorithms and quantum error correction in detail. We are often interested in the amount of resources used by a computer to solve a problem, and we refer to this as the complexity of the computation. An important resource for a computer is time. Another resource is space, which refers to the amount of memory used by the computer in performing the computation. We measure the amount of a resource used in a computation for solving a given problem as a function of the length of the input of an instance of that problem.

Kamil A. Valiev

Michele Mosca, Richard Jozsa, Andrew M. Steane +1 more

Information is stored, transmitted and processed always by physical means. Thus the concept of information and computation can be properly formulated only in the context of a physical theory and the study of information processing requires experimentation . It is clear that if computers are to become much smaller in the future, their description must be given by quantum mechanics. Somewhat more surprising is the fact that quantum information processing can be qualitatively different and much more powerful than its classical analogue. In the following we will explain why.

Giulio Casati, Dima L. Shepelyansky, P. Zoller +1 more

During the last ten years, Quantum Information Processing and Communication (QIPC) has established itself as one of the new hot topic fields in physics, with the potential to revolutionize many areas of science and technology. QIPC replaces the laws of classical physics applied to computation and communication with the more fundamental laws of quantum mechanics. This becomes increasingly important due to technological progress going down to smaller and smaller scales where quantum effects start to be dominant. In addition to its fundamental nature, QIPC promises to advance computing power beyond the capabilities of any classical computer, to guarantee secure communication and establish direct links to emerging quantum technologies, such as, for example, quantum based sensors and clocks. One of the outstanding features of QIPC is its interdisciplinary character: it brings together researchers from physics, mathematics and computer science. In particular, within physics we have seen the emergence of a new QIPC community, which ranges from theoretical to experimental physics, and crosses boundaries of traditionally separated disciplines such as atomic physics, quantum optics, statistical mechanics and solid state physics, all working on different and complementary aspects of QIPC. This publication covers the following topics: introduction to quantum computing; quantum logic, information and entanglement; quantum algorithms; error-correcting codes for quantum computations; quantum measurements and control; quantum communication; quantum optics and cold atoms for quantum information; quantum computing with solid state devices; theory and experiments for superconducting qubits; interactions in many-body systems: quantum chaos, disorder and random matrices; decoherence effects for quantum computing; and flature prospects of quantum information processing.