A dissipative quantum Church-Turing theorem

TL;DR

This paper proves that the evolution of open quantum systems can be efficiently simulated by unitary quantum circuits, establishing that dissipative quantum computing does not surpass the power of the standard unitary circuit model.

Contribution

It introduces a Trotter decomposition for Liouvillian dynamics with explicit error bounds, showing dissipative quantum systems are simulatable by unitary circuits, and discusses implications for quantum state preparation.

Findings

Dissipative quantum dynamics can be simulated by polynomial-sized unitary circuits.

Most quantum states cannot be prepared efficiently.

Provides a practical Trotter decomposition for Liouvillian evolution.

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.