Quantum algorithms for spin models and simulable gate sets for quantum computation

M. Van den Nest, W. Dür, R. Raussendorf, and H. J. Briegel
Phys. Rev. A 80, 052334 – Published 30 November 2009

Abstract

We present simple mappings between classical lattice models and quantum circuits, which provide a systematic formalism to obtain quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. We, e.g., present an efficient quantum algorithm for the six-vertex model as well as a two-dimensional Ising-type model. We show that classically simulating these (complex-parameter) spin models is as hard as simulating universal quantum computation, i.e., BQP complete (BQP denotes bounded-error quantum polynomial time). Furthermore, our mappings provide a framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. We, e.g., show that the simulability of Valiant’s match gates can be recovered by using the solvability of the free-fermion eight-vertex model.

  • Figure
  • Received 1 August 2008

DOI:https://doi.org/10.1103/PhysRevA.80.052334

©2009 American Physical Society

Authors & Affiliations

M. Van den Nest1, W. Dür2,3, R. Raussendorf4, and H. J. Briegel2,3

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
  • 2Institut für Quantenoptik und Quanteninformation, Österreichischen Akademie der Wissenschaften, Innsbruck, Austria
  • 3Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
  • 4Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Rd., Vancouver, British Columbia, Canada V6T 1Z1

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Issue

Vol. 80, Iss. 5 — November 2009

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