Many worlds, the cluster-state quantum computer, and the problem of the preferred basis

Michael E Cuffaro

doi:10.1016/j.shpsb.2011.11.007

Abstract

I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.

Highlights

The source of quantum computational ‘speedup’—the ability of a quantum computer to achieve, for some problem domains,1 a dramatic reduction in processing time over any known classical algorithm—is still a matter of debate
Unlike classical parallelism, where multiple circuits each built to compute f (x) are executed simultaneously, here a single f (x) circuit is employed to evaluate the function for multiple values of x simultaneously, by exploiting the ability of a quantum computer to be in superpositions of different states (Nielsen and Chuang, 2000, p. 31)
David Mermin is, perhaps, the most cautious with respect to the significance of this ‘quantum parallelism’: One cannot say that the result of the calculation is 2n evaluations of f, though some practitioners of quantum computation are rather careless about making such a claim

Summary

Introduction

The source of quantum computational ‘speedup’—the ability of a quantum computer to achieve, for some problem domains, a dramatic reduction in processing time over any known classical algorithm—is still a matter of debate. While Steane is correct, I will argue that the problem that the cluster state model presents to the many worlds explanation of quantum computation runs deeper than this. Second: alternative explanations of quantum computation exist which, unlike the many worlds explanation, are compatible with both the network and cluster state model. The quantum parallelism thesis, and the many worlds explanation of quantum computation that is so often associated with it, are undoubtedly of great heuristic value for the purposes of algorithm analysis and design, at least with regard to the network model. This is a fact which I should not be misunderstood as disputing.

A Simple Quantum Algorithm

Neo-Everett and Quantum Computing

Cluster State Quantum Computing

The Legitimacy of the Many Worlds Explanation for the Network Model

Conclusion