### Abstract

We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both approaches, we show that the output state of the algorithm, after long enough time, is the desired equilibrium. We present a numerical analysis of one of these approaches for small systems. We show how equilibrium (time-)correlation functions can be efficiently estimated on a quantum computer, given a preparation of the equilibrium state. The quantum algorithms that we present are hard to simulate on a classical computer. This indicates that they could provide an exponential speedup over what can be achieved with a classical device.

Original language | English |
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Article number | 022301 |

Pages (from-to) | 022301-1 - 022301-22 |

Number of pages | 22 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 61 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2000 |

Externally published | Yes |

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## Cite this

Terhal, B. M., & DiVincenzo, D. P. (2000). Problem of equilibration and the computation of correlation functions on a quantum computer.

*Physical Review A - Atomic, Molecular, and Optical Physics*,*61*(2), 022301-1 - 022301-22. [022301]. https://doi.org/10.1103/PhysRevA.61.022301