An Algorithmic Construction of Quantum Circuits of High Descriptive Complexity

  • Authors:

  • Willem L. Fouché

  • Affiliations:

  • Department of Decision Sciences, University of South Africa, Pretoria, South Africa

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2008

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Abstract

We discuss an algorithmic construction which, for any finite but universal set of computable quantum gates and a given measurement basis, will produce a rational quantum circuit whose shortest @e-approximations from products of instances of the gates have sizes which grow at least exponentially in the input sizes of the circuits and logarithmically in the reciprocal of @e. We also discuss the constructive content of the Solovay-Kitaev theorem by considering the algorithmic enumeration of all quantum circuits of a given input size.