Parallel execution of quantum gates in a long linear ion chain via Rydberg mode shaping

TL;DR

This paper introduces a method for executing multiple quantum gates simultaneously in a long ion chain by using Rydberg states to shape vibrational modes, enabling scalable quantum computing.

Contribution

It presents a novel approach to mode shaping in ion chains using Rydberg excitation, allowing parallel quantum gate operations with high fidelity.

Findings

Modes can be localized on sub-crystals for independent manipulation

Parallel gates achieve high fidelity in theoretical models

Rydberg mode shaping is feasible in realistic experimental setups

Abstract

We present a mechanism that permits the parallel execution of multiple quantum gate operations within a single long linear ion chain. Our approach is based on large coherent forces that occur when ions are electronically excited to long-lived Rydberg states. The presence of Rydberg ions drastically affects the vibrational mode structure of the ion crystal giving rise to modes that are spatially localized on isolated sub-crystals which can be individually and independently manipulated. We theoretically discuss this Rydberg mode shaping in an experimentally realistic setup and illustrate its power by analyzing the fidelity of two conditional phase flip gates executed in parallel. Our scheme highlights a possible route towards large-scale quantum computing via vibrational mode shaping which is controlled on the single ion level.