Correcting errors in a quantum gate with pushed ions via optimal control

TL;DR

This paper investigates the pushing gate in trapped ions, modeling errors with a harmonic approximation, and applies quantum optimal control to suppress errors, achieving high fidelity for fault-tolerant quantum computing.

Contribution

It introduces a time-dependent harmonic model for the pushing gate and demonstrates how optimal control can mitigate errors to improve fidelity.

Findings

Nonlinearities in pushing force affect adiabaticity significantly.

Optimal control techniques can suppress gate errors effectively.

High fidelity gates compatible with fault-tolerance are achievable.

Abstract

We analyze in detail the so-called "pushing gate" for trapped ions, introducing a time dependent harmonic approximation for the external motion. We show how to extract the average fidelity for the gate from the resulting semi-classical simulations. We characterize and quantify precisely all types of errors coming from the quantum dynamics and reveal for the first time that slight nonlinearities in the ion-pushing force can have a dramatic effect on the adiabaticity of gate operation. By means of quantum optimal control techniques, we show how to suppress each of the resulting gate errors in order to reach a high fidelity compatible with scalable fault-tolerant quantum computing.