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Quantum computers

David Deutsch

Published Jun 1, 1987• 0 citations
Publisher

Abstract

Abstract A number of research programs with widely different motivations have, during the last few years been coming to a conclusion that is startling to some, and which others say they have suspected all along: that the theory of computation is connected at many levels, including the most fundamental, to physics. In particular it has connections with our deepest and most powerful physical theory, quantum theory.

DOI
10.1093/combul/29.2.24

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Abstract A number of research programs with widely different motivations have, during the last few years been coming to a conclusion that is startling to some, and which others say they have suspected all along: that the theory of computation is connected at many levels, including the most fundamental, to physics. In particular it has connections with our deepest and most powerful physical theory, quantum theory.
This book had as its main objective to discuss how (quantum) physics concepts could be used in a relevant way in the modeling of a variety of economics/finance and psychology-based processes. For those readers who have come to read this conclusion, without skipping its “backbone,” we would like to say “thank you” for keeping with us until the end. The possible claim, which says that social science driven dynamics would need analyzing with techniques from the natural sciences, may well have been tempered with this book. Although quantum physics as a theory of prediction is one of the most successful theories humankind ever devised, it is not unreasonable to suggest that the number of foundational interpretations of quantum physics is sizable. Consider now the following natural question: “How can a theory with such a wide diversity of foundational interpretations serve to inform and elucidate a non-cognate area of research (like economics or psychology)?” Indeed, we should want to stand upright and write, without hesitation, the words “non-cognate.” No theory in social science can come close to the predictive power of quantum physics. However, very few social science theories are “plagued” by foundational issues of such depth as quantum physics. As an example, consider the issue of why quantum physical wave functions do have to be complex valued. Do physicists have a satisfactory answer to this very basic question? A theory of such predictive power has a partial differential equation, the Schrödinger equation, which cannot be rigorously derived. However, in economics and finance we strive to build theoretical edifices with the utmost respect for rigor.
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.
Abstract We arrive at the centennial of modern quantum mechanics. In about the last third of that century, we have been busy connecting quantum theory with the theory of information and the theory of computing, and with trying to turn quantum phenomena into quantum technologies. We have been talking about the quantum computer for most this trimester (i.e. for the last third-century of the history of quantum physics). Where are we at with this fantastic device? Here I give a few reflections on this question.
"Information is physical and any processing of information is always performed by physical means," an innocent-sounding statement, but its consequences are profound. When quantum effects become important, for example, at the level of single atoms and photons, the classical theory of computation becomes fundamentally inadequate. Entirely new modes of computation and information processing become possible. In the last few years there has been an explosion of theoretical and experimental research in quantum computation. In this brief review we describe some of these developments.
The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.