Universal simulation of Hamiltonians using a finite set of control operations

  • Authors:

  • Pawel Wocjan;Martin Rötteler;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;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

Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this property and present a sufficient condition in terms of group characters. We give examples of such groups in dimension 2 and 3. Furthermore, we show that it is possible to simulate an arbitrary bipartite interaction by a given one using such groups acting locally on the subsystems.