Analysis of ion chain sympathetic cooling and gate dynamics

TL;DR

This paper analyzes optimal sympathetic cooling strategies for long trapped-ion chains, balancing cooling efficiency and gate performance, and provides practical guidelines for parameter selection in quantum computing applications.

Contribution

It offers analytical and computational insights into cooling placement, frequency, and trade-offs, advancing the understanding of sympathetic cooling in large ion chains.

Findings

Optimal coolant placement at chain center improves cooling efficiency.

Frequent cooling during circuit execution enhances performance when qubit coherence is long.

Perturbative bounds on mode cooling limits guide parameter choices.

Abstract

Sympathetic cooling is a technique often employed to mitigate motional heating in trapped-ion quantum computers. However, choosing system parameters such as number of coolants and cooling duty cycle for optimal gate performance requires evaluating trade-offs between motional errors and other slower errors such as qubit dephasing. The optimal parameters depend on cooling power, heating rate, and ion spacing in a particular system. In this study, we aim to analyze best practices for sympathetic cooling of long chains of trapped ions using analytical and computational methods. We use a case study to show that optimal cooling performance is achieved when coolants are placed at the center of the chain and provide a perturbative upper-bound on the cooling limit of a mode given a particular set of cooling parameters. In addition, using computational tools, we analyze the trade-off between the number of coolant ions in a chain and the center-of-mass mode heating rate. We also show that cooling as often as possible when running a circuit is optimal when the qubit coherence time is otherwise long. These results provide a roadmap for how to choose sympathetic cooling parameters to maximize circuit performance in trapped ion quantum computers using long chains of ions.