Universal simulation of Markovian quantum dynamics

Dave Bacon, Andrew M. Childs, Isaac L. Chuang, Julia Kempe, Debbie W. Leung, and Xinlan Zhou
Phys. Rev. A 64, 062302 – Published 9 November 2001
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Abstract

Although the conditions for performing arbitrary unitary operations to simulate the dynamics of a closed quantum system are well understood, the same is not true of the more general class of quantum operations (also known as superoperators) corresponding to the dynamics of open quantum systems. We propose a framework for the generation of Markovian quantum dynamics and study the resources needed for universality. For the case of a single qubit, we show that a single nonunitary process is necessary and sufficient to generate all unital Markovian quantum dynamics, whereas a set of processes parametrized by one continuous parameter is needed in general. We also obtain preliminary results for the unital case in higher dimensions.

  • Received 15 August 2000

DOI:https://doi.org/10.1103/PhysRevA.64.062302

©2001 American Physical Society

Authors & Affiliations

Dave Bacon1,2, Andrew M. Childs3,4, Isaac L. Chuang4, Julia Kempe1,5,6, Debbie W. Leung4,7,8, and Xinlan Zhou4,9

  • 1Department of Chemistry, University of California, Berkeley, California 94720
  • 2Department of Physics, University of California, Berkeley, California 94720
  • 3Physics Department, California Institute of Technology, Pasadena, California 91125
  • 4IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120
  • 5Department of Mathematics, University of California, Berkeley, California 94720
  • 6École Nationale Superieure des Télécommunications, Paris, France
  • 7Quantum Entanglement Project, ICORP, JST, Edward Ginzton Laboratory, Stanford University, Stanford, California 94305
  • 8IBM T. J. Watson Research Center, Yorktown Heights, New York 10598
  • 9Applied Physics Department, Stanford University, Stanford, California 94305

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Vol. 64, Iss. 6 — December 2001

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