Fast phase gates with trapped ions

TL;DR

This paper demonstrates a method to perform rapid two-qubit phase gates with trapped ions using smooth, state-dependent forces that avoid motional excitation, leveraging quadratic invariants and Lewis-Riesenfeld phases for precise control.

Contribution

The authors introduce a novel approach for faster-than-adiabatic phase gates with trapped ions that ensures no motional excitation, based on explicit time-dependent forces derived from invariants.

Findings

Faster-than-adiabatic phase gates achieved

No residual motional excitation in the harmonic limit

Explicit force functions designed for desired phases

Abstract

We implement faster-than-adiabatic two-qubit phase gates using smooth state-dependent forces. The forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic, small-oscillations limit. They are simple, explicit functions of time and the desired logical phase of the gate, and are based on quadratic invariants of motion and Lewis-Riesenfeld phases of the normal modes.