Preparing Thermal States of Quantum Systems by Dimension Reduction

Ersen Bilgin and Sergio Boixo
Phys. Rev. Lett. 105, 170405 – Published 22 October 2010

Abstract

We present an algorithm that prepares thermal Gibbs states of one dimensional quantum systems on a quantum computer without any memory overhead, and in a time significantly shorter than other known alternatives. Specifically, the time complexity is dominated by the quantity Nh/T, where N is the size of the system, h is a bound on the operator norm of the local terms of the Hamiltonian (coupling energy), and T is the temperature. Given other results on the complexity of thermalization, this overall scaling is likely optimal. For higher dimensions, our algorithm lowers the known scaling of the time complexity with the dimension of the system by one.

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  • Received 24 August 2010

DOI:http://dx.doi.org/10.1103/PhysRevLett.105.170405

© 2010 The American Physical Society

Authors & Affiliations

Ersen Bilgin,* and Sergio Boixo,†

  • Institute of Quantum Information, California Institute of Technology, Pasadena, California, 91125, USA

  • *ersen@caltech.edu
  • boixo@caltech.edu

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Vol. 105, Iss. 17 — 22 October 2010

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