Percolation, Renormalization, and Quantum Computing with Nondeterministic Gates

K. Kieling, T. Rudolph, and J. Eisert
Phys. Rev. Lett. 99, 130501 – Published 25 September 2007

Abstract

We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of nondeterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single-qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.

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  • Received 20 December 2006

DOI:https://doi.org/10.1103/PhysRevLett.99.130501

©2007 American Physical Society

Authors & Affiliations

K. Kieling, T. Rudolph, and J. Eisert

  • QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom
  • and Institute for Mathematical Sciences, Imperial College London, Prince’s Gate, London SW7 2PE, United Kingdom

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Issue

Vol. 99, Iss. 13 — 28 September 2007

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