Implementing conventional and unconventional nonadiabatic geometric quantum gates via SU(2) transformations

TL;DR

This paper introduces a versatile protocol for designing time-dependent Hamiltonians to implement both conventional and unconventional nonadiabatic geometric quantum gates using SU(2) transformations, enhancing speed and noise resilience.

Contribution

The authors develop an inverse engineering method based on SU(2) transformations for geometric quantum gates, allowing flexible control and improved performance in nitrogen-vacancy centers.

Findings

Achieves faster gate operations with reduced environmental noise impact.

Enables implementation of both conventional and unconventional geometric gates.

Provides a control protocol adaptable to NV center systems.

Abstract

We propose a simple but versatile protocol to engineer time-dependent Hamiltonians inversely for geometric quantum computation. By utilizing SU(2) transformation, a speedup goal on gate operation is achieved with more freedom to design the control parameters. As an application, this protocol enables the conventional and unconventional nonadiabatic geometric quantum gates with desired evolution paths by controlling the microwave pulses in the diamond nitrogen-vacancy center system. We show that the inversely designed Hamiltonian can fulfill the geometric gate with more economical evolution time and further reduces the influence of the environment noise on gate fidelity.