# Stuttgart 2012 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# Q: Fachverband Quantenoptik und Photonik

## Q 49: Quanteninformation: Konzepte und Methoden 5

### Q 49.2: Vortrag

### Donnerstag, 15. März 2012, 14:15–14:30, V7.01

**A dissipative quantum Church-Turing theorem** — •Martin Kliesch^{1}, Thomas Barthel^{1}, Christian Gogolin^{1}, Michael Kastoryano^{2}, and Jens Eisert^{1} — ^{1}Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany — ^{2}Niels Bohr Institute, University of Copenhagen, Denmark

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.