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

Abstract

A simple yet versatile protocol to inversely engineer time-dependent Hamiltonian is proposed. By utilizing SU(2) transformation, a given speedup goal of gate operation can be achieved with larger freedom to select the control parameters. As an application, this protocol is adopted to realize conventional and unconventional nonadiabatic geometric quantum gates with any desired evolution paths by controlling the pulses in the diamond nitrogen-vacancy (NV) center system. We show that the designed gate can realize geometric quantum computation with a more economical evolution time that decreases the influence of noise on gate operation.