Quantum Simulations with Cold Trapped Ions

TL;DR

This paper reviews recent theoretical and experimental advances in using cold trapped ions for quantum simulations, covering diverse models like spin systems, Bose-Hubbard, and relativistic quantum fields.

Contribution

It provides a comprehensive overview of current proposals and experiments in quantum simulation with trapped ions, highlighting their versatility and potential.

Findings

Demonstrated simulation of spin models such as the transverse Ising model

Explored quantum simulation of Bose-Hubbard and Frenkel-Kontorova models

Reviewed quantum field and relativistic effects simulated with trapped ions

Abstract

The control of internal and motional quantum degrees of freedom of laser cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g., the quantum transverse Ising model, or a neural network), the Bose-Hubbard Hamiltonian, the Frenkel-Kontorova model, and quantum fields and relativistic effects.