Dissipative quantum Church-Turing theorem.


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Kliesch, M; Barthel, T; Gogolin, C; Kastoryano, M; Eisert, J

Published Date

  • September 12, 2011

Published In

Volume / Issue

  • 107 / 12

Start / End Page

  • 120501 -

PubMed ID

  • 22026760

Pubmed Central ID

  • 22026760

Electronic International Standard Serial Number (EISSN)

  • 1079-7114

International Standard Serial Number (ISSN)

  • 0031-9007

Digital Object Identifier (DOI)

  • 10.1103/physrevlett.107.120501


  • eng