Analytic Solution Of NHQC+ And Its Application To Superconducting Qubits

Quantum computation is regarded as a new calculation method with the potential advantages over classical computation.However,quantum computation has inevitable disadvantages because of the experimental conditions.To realize more accurate and robust quantum computation,geometric quantum computation,based on the geometric phase,has been proposed.According to different types of geometric phases and different evolutions,non-adiabatic holonomic quantum computation(NHQC),induced by nonadiabatic non-Abelian geometric phases,provide a promising way towards universal quantum computation.However,NHQC is limited by the requirement of a fixed pulse area,reducing the robustness of gates against control errors.Compared with NHQC,an optimal method,called NHQC+,has been proposed.NHQC+ has its advantages in relaxing the limitation of the dynamical phase,so the scheme has weaker sensitivity to outer noises.But it still has the shortages that it’s difficult to find proper states to satisfy the von Neumann equation in some systems and using jumping pulse to vanish dynamical phase will decrease fidelity.Here,I propose an alternative approach to construct non-adiabatic holonomic gates,which is an analytic solution of NHQC+ scheme,by using an analytically solvable method without compromising the robustness against control errors and noises.Rather than solve the von Neumann equation,this approach only needs an analytic solution to directly find out the suitable auxiliary states to realize the construction of non-adiabatic holonomic gates.Thus,it’s a more convenient way to implement NHQC+ scheme.In this way,it is possible to obtain a purely geometric phase without dynamical contributions after a cyclic quantum evolution.Furthermore,this analytic solution of NHQC+ scheme can be applied to various physical platforms such as trapped ion and nitrogen-vacancy centers.As an example,we implement single and non-trial two-qubit geometric gate to realize universal analytically solvable holonomic quantum computation with superconducting circuits.Specifically,we performed a numerical simulation to show the noise robustness can be significantly improved comparing with NHQC and dynamical gate(DG)with recent superconducting experimental implementations.Therefore,this scheme provides an essential method towards the realization of robust holonomic quantum computation.