Quantum simulation of open-system dynamical maps with trapped ions

TL;DR

This paper demonstrates the experimental simulation of complex open-system quantum dynamics using trapped ions, revealing phenomena like long-range coherence and non-equilibrium phase transitions, and introduces tools for scaling up such simulations.

Contribution

It extends dynamical maps to many-particle open quantum systems and experimentally explores their complex behavior with a universal quantum simulator.

Findings

Generated long-range phase coherence in spin systems.

Observed competition between coherent and dissipative evolution.

Developed error detection tools for larger quantum simulations.

Abstract

Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to chaos. Quantum mechanical counterparts show intriguing phenomena such as dynamical localization on the single particle level. Here we extend the concept of dynamical maps to an open-system, many-particle context: We experimentally explore the stroboscopic dynamics of a complex many-body spin model by means of a universal quantum simulator using up to five ions. In particular, we generate long-range phase coherence of spin by an iteration of purely dissipative quantum maps. We also demonstrate the characteristics of competition between combined coherent and dissipative non-equilibrium evolution. This opens the door for studying many-particle non-equilibrium physics and associated dynamical phase transitions with no immediate counterpart in equilibrium condensed matter systems. An error detection and reduction toolbox that facilitates the faithful quantum simulation of larger systems is developed as a first step in this direction.