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arXiv:quant-ph/0502120 · Physical Review Letters

Efficient Quantum Computation with Probabilistic Quantum Gates

Luming Duan, Robert Raussendorf

Published Aug 17, 2005• 185 citations
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Abstract

With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability p. The required computational overhead scales efficiently both with 1/p and n, where n is the number of qubits in the computation. This approach provides an efficient way to combat noise in a class of quantum computation implementation schemes, where the dominant noise leads to probabilistic signaled errors with an error probability 1-p far beyond any threshold requirement.

DOI
10.1103/physrevlett.95.080503

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With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability p. The required computational overhead scales efficiently both with 1/p and n, where n is the number of qubits in the computation. This approach provides an efficient way to combat noise in a class of quantum computation implementation schemes, where the dominant noise leads to probabilistic signaled errors with an error probability 1-p far beyond any threshold requirement.
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The cluster state model for quantum computation has paved the way for schemes that allow scalable quantum computing, even when using non-deterministic quantum gates. Here the initial step is to prepare a large entangled state using non-deterministic gates. A key question in this context is the relative efficiencies of different 'strategies', i.e. in what order should the non-deterministic gates be applied, in order to maximize the size of the resulting cluster states? In this paper we consider this issue in the context of 'large' cluster states. Specifically, we assume an unlimited resource of qubits and ask what the steady state rate at which 'large' clusters are prepared from this resource is, given an entangling gate with particular characteristics. We measure this rate in terms of the number of entangling gate operations that are applied. Our approach works for a variety of different entangling gate types, with arbitrary failure probability. Our results indicate that strategies whereby one preferentially bonds together clusters of identical length are considerably more efficient than those in which one does not. Additionally, compared to earlier analytic results, our numerical study offers substantially improved resource scaling.