Transformation of quantum states using uniformly controlled rotations

  • Authors:

  • Mikko Möttönen;Juha J. Vartiainen;Ville Bergholm;Martti M. Salomaa

  • Affiliations:

  • Materials Physics Laboratory, Helsinki University of Technology, Helsinki, Finland;Materials Physics Laboratory, Helsinki University of Technology, Helsinki, Finland;Materials Physics Laboratory, Helsinki University of Technology, Helsinki, Finland;Materials Physics Laboratory, Helsinki University of Technology, Helsinki, Finland

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

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Abstract

We consider a unitary transformation which maps any given state of an n-qubit quantum register into another one. This transformation has applications in the initialization of a quantum computer, and also in some quantum algorithms. Employing uniformly controlled rotations, we present a quantum circuit of 2n+2 - 4n - 4 CNOT gates and 2n+2 - 5 one-qubit elementary rotations that effects the state transformation. The complexity of the circuit is noticeably lower than the previously published results. Moreover, we present an analytic expression for the rotation angles needed for the transformation.