Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

Michael A. Nielsen, Michael J. Bremner, Jennifer L. Dodd, Andrew M. Childs, and Christopher M. Dawson
Phys. Rev. A 66, 022317 – Published 30 August 2002
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Abstract

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

  • Received 14 September 2001

DOI:https://doi.org/10.1103/PhysRevA.66.022317

©2002 American Physical Society

Authors & Affiliations

Michael A. Nielsen1,*, Michael J. Bremner1,†, Jennifer L. Dodd1,‡, Andrew M. Childs1,2,§, and Christopher M. Dawson1,∥

  • 1Centre for Quantum Computer Technology and Department of Physics, University of Queensland, Brisbane 4072, Queensland, Australia
  • 2Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

  • *Electronic address: nielsen@physics.uq.edu.au
  • Electronic address: bremner@physics.uq.edu.au
  • Electronic address: jdodd@physics.uq.edu.au
  • §Electronic address: amchilds@mit.edu
  • Electronic address: dawson@physics.uq.edu.au

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Vol. 66, Iss. 2 — August 2002

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