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Dissipative Quantum Church-Turing Theorem

M. Kliesch, T. Barthel, C. Gogolin, M. Kastoryano, and J. Eisert
Phys. Rev. Lett. 107, 120501 – Published 12 September 2011; Erratum Phys. Rev. Lett. 109, 119904 (2012)
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Abstract

We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Church-Turing theorem, since it implies that under natural assumptions, such as weak coupling to an environment, the dynamics of an open quantum system can be simulated efficiently on a quantum computer. Formally, we introduce a Trotter decomposition for Liouvillian dynamics and give explicit error bounds. This constitutes a practical tool for numerical simulations, e.g., using matrix-product operators. We also demonstrate that most quantum states cannot be prepared efficiently.

  • Received 10 June 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.120501

© 2011 American Physical Society

Erratum

Erratum: Dissipative Quantum Church-Turing Theorem [Phys. Rev. Lett. 107, 120501 (2011)]

M. Kliesch, T. Barthel, C. Gogolin, M. Kastoryano, and J. Eisert
Phys. Rev. Lett. 109, 119904 (2012)

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Quantum simulation hits the open road

Published 12 September 2011

Techniques for using a quantum computer to simulate another quantum system will work even when the modeled system is not isolated from its environment.

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Authors & Affiliations

M. Kliesch1,2, T. Barthel1,2, C. Gogolin1,2, M. Kastoryano3, and J. Eisert1,2

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
  • 2Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
  • 3Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark

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Issue

Vol. 107, Iss. 12 — 16 September 2011

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Heating up of Superconductors
January 27, 2017

This collection marks the 30th anniversary of the discovery of high-temperature superconductors. The papers selected highlight some of the advances that have been made to date, both in understanding why these compounds behave in the way they do, and in utilizing them in applications. The papers included in the collection have been made free to read.

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