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Cluster-state quantum computation

by Michael Nielsen on April 15, 2005

One of my main areas of research interest for the past few years has been measurement-based models of quantum computation. In the standard accounts of quantum computing, a quantum computer is presented as a device that gets its power by performing coherent manipulations of superpositions of computational states, before a final measurement step destroys the superposition, singling out a single computational state to be read out.

Measurement-based quantum computing turns this picture on its head. In such a model, there are no coherent manipulations of superpositions. Instead, it’s just all measurements, all the time. In Debbie Leung’s memorable phrase, we compute by “pinging Nature”.

I’ve just written a short pedagogical review of one of these models, the so-called “one-way quantum computer”, or “cluster-state model” of quantum computation. A simple version of this model was recently implemented in the lab, as reported in Nature by the Zeilinger group.

The review is written to be accessible to anyone with a thorough grounding in basic quantum mechanics. The main part of the review is spent explaining what a quantum computer is, what the cluster state model is, and how clusters can be used to simulate an ordinary quantum computer. At the end, I also explain two new results: (1) a no-go theorem which, subject to some caveats (see paper), forbids us from obtaining the cluster experimentally by cooling a physical system to the ground state; and (2) a proof that clusters must be prepared in two or more dimensions if they are to be useful for quantum computing.

The review was written for a festschrift in honour of Tony Bracken and Angas Hurst, two well-known Australian mathematical physicists. Tony was my fourth-year honours thesis advisor, for which he suggested a wonderful topic: whether there is any connection between sometimes-negative “probability” distribution functions, like the Wigner function, and the Bell inequalities. It was a great topic for a student, combining a fundamental physical aspect with beautiful mathematics, and requiring only a little background to get started.

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