Colloquium: Trapped ions as quantum bits -- essential numerical tools

TL;DR

This paper reviews numerical tools for optimizing control and understanding quantum dynamics of trapped ions, enabling virtual experiments and improved quantum gate design in ion-trap systems.

Contribution

It introduces advanced numerical methods for controlling and simulating trapped ion quantum systems, including inverse problem solutions and quantum optimal control techniques.

Findings

Efficient solvers for time-dependent and independent problems

Methods for shaping motional wavefunctions and optimizing quantum gates

Provision of code and tools for virtual quantum experiments

Abstract

Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well known Hamiltonian. In this colloquium, we present powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap. We then delve into solving inverse problems, when optimizing trapping potentials for ions. Our presentation is complemented by a quantum mechanical treatment of the wavepacket dynamics of a trapped ion. Efficient numerical solvers for both time-independent and time-dependent problems are provided. Shaping the motional wavefunctions and optimizing a quantum gate is realized by the application of quantum optimal control techniques. The numerical methods presented can also be used to gain an intuitive understanding of quantum experiments with trapped ions by performing virtual simulated experiments on a personal computer. Code and executables are supplied as supplementary online material (http://kilian-singer.de/ent).