Quantum computing and polynomial equations over the finite field Z2

  • Authors:

  • Christopher M. Dawson;Andrew P. Hines;Duncan Mortimer;Henry L. Haselgrove;Michael A. Nielsen;Tobias J. Osborne

  • Affiliations:

  • School of Physical Sciences, The University of Queensland, Brisbane, Queensland, Australia;School of Physical Sciences, The University of Queensland, Brisbane, Queensland, Australia;School of Physical Sciences, The University of Queensland, Brisbane, Queensland, Australia;School of Physical Sciences, The University of Queensland, Brisbane, Queensland, Australia and Information Sciences Laboratory, Defence Science and Technology Organisation, Edinburgh, Australia;School of Physical Sciences, School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, Queensland, Australia;School of Mathematics, University of Bristol, University Walk, Bristol, United Kingdom

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2005

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Abstract

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP ⊆ PP and BQP ⊆ PP.