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International Journal of Circuit Theory and Applications

Nanoscopic quantum networks: collective versus selective control

G�nter Mahler, Alexander Otte

Published Jan 1, 2001• 4 citations
Publisher

Abstract

Present-day information processing is based on the rules of classical physics. If the ubiquitous superposition principle of quantum mechanics could be harnessed, quite different and surprising rules would be at our disposal. They would give rise to the celebrated quantum parallelism allowing, e.g. for an increased efficiency of quantum over classical computing. To achieve this goal there are at least two different paradigms which could be exploited: ‘selective control’ and ‘collective control’. The latter should be an interesting alternative for nanoscopic quantum networks. Copyright © 2001 John Wiley & Sons, Ltd.

DOI
10.1002/1097-007x(200101/02)29:1<93::aid-cta135>3.0.co;2-5

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Present-day information processing is based on the rules of classical physics. If the ubiquitous superposition principle of quantum mechanics could be harnessed, quite different and surprising rules would be at our disposal. They would give rise to the celebrated quantum parallelism allowing, e.g. for an increased efficiency of quantum over classical computing. To achieve this goal there are at least two different paradigms which could be exploited: ‘selective control’ and ‘collective control’. The latter should be an interesting alternative for nanoscopic quantum networks. Copyright © 2001 John Wiley & Sons, Ltd.
Present-day computers work on the principles of classical mechanics. Imagine a coin in the classical regime. When we toss the coin, it can take up either of these two states: “head” (H) or “tail” (T). However, in a quantum world, a coin, or rather a quantum one, can exist in both the states “head” and “tail” simultaneously. This property of quantum mechanical objects—existing in multiple states simultaneously—is known as superposition . Similarly, quantum mechanical objects can exhibit a much stronger correlation than their classical counterparts through the phenomenon of entanglement . Using entanglement, two or more quantum particles can be linked in perfect unison, even when they are placed at opposite ends of the universe. Quantum computing harnesses and exploits the laws of quantum mechanics, especially superposition, entanglement, and interference, to process information. An important idea in quantum computing is to collapse a probability distribution toward specific measurement states. Quantum interference is a by-product of quantum superposition, and it helps bias quantum measurement toward specific quantum states.
I give an informal discussion of the nature of quantum computation, arguing that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum computers to "perform many computations simultaneously" except in a highly qualified and to some extent misleading sense. Quantum computation is therefore not well described by interpretations of quantum mechanics which invoke the concept of vast numbers of parallel universes. Rather, entanglement makes available types of computation process which, while not exponentially larger than classical ones, are unavailable to classical systems.
Abstract Since quantum systems interact with their environment permanently or within a measurement process, there is much interest in concepts of open quantum system modelling. In this paper we give an overview on three different concepts in order to address this problem in the context of the network paradigm. Furthermore the modelling of spatially localized decoherence processes within the stochastic diffusion wave equation approach of Gisin et al. is briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.