Fast and efficient exact synthesis of single-qubit unitaries generated by clifford and T gates

  • Authors:

  • Vadym Kliuchnikov;Dmitri Maslov;Michele Mosca

  • Affiliations:

  • Institute for Quantum Computing and School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;National Science Foundation, Arlington, Virginia and Institute for Quantum Computing, and Dept. of Physics & Astronomy, University of Waterloo, Waterloo, Ontario, Canada;Institute for Quantum Computing and Dept. of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada and Perimeter Insitute for Theoretical Physics, Waterloo, Ontario, ...

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2013

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Abstract

In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring Z[1/√2, i], in the single-qubit case. We report an efficient synthesis algorithm, with an exact optimality guarantee on the number of Hadamard and T gates used. We conjecture that the equivalence of the sets of unitaries implementable by circuits over the Clifford and T library and unitaries over the ring Z[1/√2, i] holds in the n-qubit case.