Simulating open quantum systems: from many-body interactions to stabilizer pumping

TL;DR

This paper presents a theoretical framework for simulating open quantum systems using trapped ions, enabling the study of complex many-body and topological models through digital quantum simulation techniques.

Contribution

It introduces a comprehensive theoretical approach for digital simulation of open quantum systems with trapped ions, including schemes for topological quantum models.

Findings

Framework for open-system simulation with trapped ions

Concrete schemes for Kitaev's toric code and color code models

Protocols adaptable to scalable 2D ion-trap architectures

Abstract

In a recent experiment, Barreiro et al. demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions [Nature 470, 486 (2011)]. Using up to five ions, single- and multi-qubit entangling gate operations were combined with optical pumping in stroboscopic sequences. This enabled the implementation of both coherent many-body dynamics as well as dissipative processes by controlling the coupling of the system to an artificial, suitably tailored environment. This engineering was illustrated by the dissipative preparation of entangled two- and four-qubit states, the simulation of coherent four-body spin interactions and the quantum non-demolition measurement of a multi-qubit stabilizer operator. In the present paper, we present the theoretical framework of this gate-based ("digital") simulation approach for open-system dynamics with trapped ions. In addition, we discuss how within this simulation approach minimal instances of spin models of interest in the context of topological quantum computing and condensed matter physics can be realized in state-of-the-art linear ion-trap quantum computing architectures. We outline concrete simulation schemes for Kitaev's toric code Hamiltonian and a recently suggested color code model. The presented simulation protocols can be adapted to scalable and two-dimensional ion-trap architectures, which are currently under development.