Non-adiabatic Holonomic Quantum Computation In The Selective Rydberg Pumping Mechanism

In the past two decades,due to the unique advantages of quantum computers,a large number of researches on the establishment of scalable and functional quantum computers have been stimulated.The realization of a set of universal quantum gates with high fidelity is the key to the realization of quantum computers.However,the errors of the quantum system will inevitably affect the fidelity of the quantum gate,and the propagation of these inaccurate control errors may soon destroy the actual implementation.Because of its robustness to control inaccuracy and high-speed implementation,non-adiabatic holonomic quantum computation has become a promising way of quantum computers.It was soon proved by experiments in various quantum systems that non-adiabatic holonomic quantum computation.At present,the selective Rydberg pumping mechanism is increasingly popular,which can selectively excite the target quantum states of neutral atoms and freeze the evolution of other non target quantum states.The SRP mechanism takes advantage of the combined effects of multi-frequency driving fields and strong dipole-dipole interaction,in which the first-order Rabi coupling replaces traditional second-order dynamics in the Rydberg antiblockade.Since the first-order Rabi coupling is usually much larger than the secondorder interaction required by the Rydberg antiblockade,the scheme based on Rydberg anti blockade can be greatly accelerated and the attenuation of other excited Rydberg states can be reduced at the same time.The SRP mechanism opens a new chapter for the quantum information processing of neutral protons.In this paper,we propose a reliable scheme of selective Rydberg pumping mechanism.The selective Rydberg pumping mechanism The selective Rydberg pumping mechanism eliminates the non-resonance term by rotating wave approximation.In the case of large detuning,the high frequency oscillation term is eliminated by rotating wave approximation,and the effective Hamiltonian of the system is obtained,and the layout number of the ground states in its evolution process is calculated.According to the effective Hamiltonian of the system,the two-qubit holonomic quantum gate is calculated,and the fidelity is calculated.Finally,we verify whether the double quantum gate meets the conditions of non-adiabatic holonomic quantum gates.After verification,it meets the cycle conditions and pure geometric conditions.It is proved that it is a two-qubit non-adiabatic holonomic quantum gate.However,the traditional parameter setting is incomplete,which reduces the high fidelity of quantum gate.In order to overcome this shortcoming,we further studied a reliable scheme of the selective Rydberg pumping mechanism combined with the Gaussian time-dependent control technology,which controls the time-dependent change of the interaction intensity,and the highly selective coupling between the different resonance terms of the composite quantum system.At the same time,the non-resonance terms are effectively suppressed.The target Hamiltonian is calculated and quantum gate is constructed based on the target Hamiltonian.It is found that the cyclic evolution can be realized in a short time,and has stable high fidelity,which can broaden the application of Rydberg atom in quantum computation.