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Simulation of classical thermal states on a quantum computer: A transfer-matrix approach

Man-Hong Yung, Daniel Nagaj, James D. Whitfield, and Alán Aspuru-Guzik
Phys. Rev. A 82, 060302(R) – Published 30 December 2010
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Abstract

We present a hybrid quantum-classical algorithm to simulate thermal states of classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one at a time. We identified a class of classical models for which our method is efficient and avoids potential exponential overheads encountered by Grover-like or quantum Metropolis schemes. Our algorithm also gives an exponential advantage for two-dimensional Ising models with magnetic field on a square lattice, compared with the previously known Zalka’s algorithm.

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  • Received 30 April 2010

DOI:https://doi.org/10.1103/PhysRevA.82.060302

© 2010 The American Physical Society

Authors & Affiliations

Man-Hong Yung1,2,*, Daniel Nagaj3, James D. Whitfield2, and Alán Aspuru-Guzik2,†

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
  • 2Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovakia

  • *mhyung@chemistry.harvard.edu
  • aspuru@chemistry.harvard.edu

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Issue

Vol. 82, Iss. 6 — December 2010

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