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)
Viewpoint
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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