Time-optimal unitary operations

Alberto Carlini, Akio Hosoya, Tatsuhiko Koike, and Yosuke Okudaira
Phys. Rev. A 75, 042308 – Published 10 April 2007

Abstract

Extending our previous work on time-optimal quantum state evolution [Carlini et al., Phys. Rev. Lett. 96, 060503 (2006)], we formulate a variational principle for finding the time-optimal realization of a target unitary operation, when the available Hamiltonians are subject to certain constraints dictated either by experimental or by theoretical conditions. Since the time-optimal unitary evolutions do not depend on the input quantum state this is of more direct relevance to quantum computation. We explicitly illustrate our method by considering the case of a two-qubit system self-interacting via an anisotropic Heisenberg Hamiltonian and by deriving the time-optimal unitary evolution for three examples of target quantum gates, namely, the swap of qubits, the quantum Fourier transform, and the entangler gate. We also briefly discuss the case in which certain unitary operations take negligible time.

  • Figure
  • Received 4 August 2006

DOI:https://doi.org/10.1103/PhysRevA.75.042308

©2007 American Physical Society

Authors & Affiliations

Alberto Carlini1,*, Akio Hosoya1,†, Tatsuhiko Koike2,‡, and Yosuke Okudaira1,§

  • 1Department of Physics, Tokyo Institute of Technology, Tokyo, Japan
  • 2Department of Physics, Keio University, Yokohama, Japan

  • *Electronic address: carlini@th.phys.titech.ac.jp
  • Electronic address: ahosoya@th.phys.titech.ac.jp
  • Electronic address: koike@phys.keio.ac.jp
  • §Electronic address: okudaira@th.phys.titech.ac.jp

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Issue

Vol. 75, Iss. 4 — April 2007

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