Efficient Decomposition of Quantum Gates

Juha J. Vartiainen, Mikko Möttönen, and Martti M. Salomaa
Phys. Rev. Lett. 92, 177902 – Published 29 April 2004

Abstract

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4n) which coincides with the theoretical lower bound.

  • Figure
  • Figure
  • Received 30 December 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.177902

©2004 American Physical Society

Authors & Affiliations

Juha J. Vartiainen*, Mikko Möttönen, and Martti M. Salomaa

  • Materials Physics Laboratory, Helsinki University of Technology, POB 2200 (Technical Physics), FIN-02015 HUT, Finland

  • *Electronic address: juhav@focus.hut.fi

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Vol. 92, Iss. 17 — 30 April 2004

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