Quantum algorithm for measuring the eigenvalues of U ⊗ U-1 for a black-box unitary transformation U

  • Authors:

  • Dominik Janzing;Thomas Beth

  • Affiliations:

  • Institut für Algorithmen und Kognitive Systeme, Arbeitsgruppe Quanten Computing, Universität Karlsruhe, Karlsruhe, Germany;Institut für Algorithmen und Kognitive Systeme, Arbeitsgruppe Quanten Computing, Universität Karlsruhe, Karlsruhe, Germany

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2002

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Abstract

Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure eigenvalues of U⊗U† even in this case. Running the algorithm several times allows therefore to estimate the autocorrelation function of the density of eigenstates of U. This can be applied to find periodicities in the energy spectrum of a quantum system with unknown Hamiltonian if it can be coupled to a quantum computer.