Research Of Multiple-Qubit Geometric Quantum Logic Gate In Rydberg Atom System

As an important part of quantum logic gate,multiple qubit logic gates are an essential element in the implementation of quantum computers,it has a wide range of practical applications in quantum computing.Compared with the traditional multiple-qubit logic gates which are constructed by a series of two-qubit gates and single-qubit gates,effectively and directly construct multiple-qubit logic gates are of great value to quantum computers.The multiple-qubit logic gate realized in one step can reduce the operation difficulty,save quantum resources and improve robust of the multiple-qubit gates.This paper mainly studies the scheme of directly constructing multiple-qubit logic gates by using Rydberg blockade effect on neutral Rydberg atom platform.Firstly,this paper proposes a scheme to realize multiple qubit Ck U gate in Rydberg atom system,where k denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit.This scheme makes use of LewisRiesenfeld(LR)invariant-based inverse engineering method in shortcut to adiabaticity,geometric quantum computation and zero systematic-error sensitivity optimal control theory.The geometric quantum computation considered in this scheme ensures robust to systematic errors.At the same time,compared with the adiabatic process,the inverse engineering based on shortcut to adiabaticity has further advantages in the speed of system evolution.Then,the paper extends the first scheme and proposes a scheme to directly realize multiple qubit Ck Um gate.That is,multiple control-atoms control multiple target-atoms,the scheme is also based on the Rydberg blockade effect and geometric quantum operation.The geometric quantum operation adopts the nonadiabatic holonomic quantum computation method,which breaks the strict limit of Hamiltonian in traditional nonadiabatic holonomic quantum computation,and in order to further improve the fidelity of the gates,in this paper,the unconventional nonadiabatic holonomic quantum computation is combined with the single-shot shaped pulse optimize theory to further optimize the pulse parameters,and realize a fast and robust high fidelity universal multiple qubit Ck Um gate with k control atoms and m target atoms.Finally,considering the existence of systematic error and spontaneous emission,the numerical simulation of the above two schemes with reasonable data in theory and experiment is carried out respectively.The two numerical simulation results are quite consistent with the theoretical calculation results,which verifies the feasibility of the scheme.This work can provide more alternative ways to realize the general multiple qubit logic gate based on the theory and experiment of Rydberg atom system in the future.