A dissipative quantum Church-Turing theorem

Details A dissipative quantum Church-Turing theorem A dissipative quantum Church-Turing theorem

2011-05-19

arxiv.org/abs/1105.3986v4

Phys. Rev. Lett. 107, 120501 (2011)

Physics

Quantum Physics

4 pages + 5 pages appendix, Implication 3 corrected

Scientific paper

10.1103/PhysRevLett.107.120501

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.

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