Quantum and classical parallelism in parity algorithms for ensemble quantum computers

Ralf Stadelhofer, Dieter Suter, and Wolfgang Banzhaf
Phys. Rev. A 71, 032345 – Published 28 March 2005

Abstract

The determination of the parity of a string of N binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least N2 oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor 2k, with k{1,2,,log2(N2)}, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.

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  • Received 22 October 2004

DOI:https://doi.org/10.1103/PhysRevA.71.032345

©2005 American Physical Society

Authors & Affiliations

Ralf Stadelhofer1,*, Dieter Suter2, and Wolfgang Banzhaf3

  • 1University of Dortmund Department of Computer Science, 44221 Dortmund, Germany
  • 2University of Dortmund, Department of Physics, 44221 Dortmund, Germany
  • 3Memorial University of Newfoundland, Department of Computer Science, St. John’s, NL, A1B 3X5, Canada

  • *Electronic address: ralf.stadelhofer@udo.edu

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Vol. 71, Iss. 3 — March 2005

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