Classical simulation of noninteracting-fermion quantum circuits

Barbara M. Terhal and David P. DiVincenzo
Phys. Rev. A 65, 032325 – Published 1 March 2002
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Abstract

We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [in Proceedings of the 33rd ACM Symposium on the Theory of Computing (2001), p. 114] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits [E. Knill, R. Laflamme, and G. Milburn, Nature (London) 409, 46 (2001)].

  • Received 10 August 2001

DOI:https://doi.org/10.1103/PhysRevA.65.032325

©2002 American Physical Society

Authors & Affiliations

Barbara M. Terhal and David P. DiVincenzo

  • IBM, T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598

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Issue

Vol. 65, Iss. 3 — March 2002

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