Fast Implementation Of A C-NOT~N Gate In The Rydberg-atom System

In recent years,the research on Rydberg atoms has attracted much attention.In the neutral atomic system,due to the existence of the Rydberg blockade effect,only one atom can be excited to Rydberg state within the blockade radius,which provides an effective method for multi-atom control.Moreover,the Rydberg blockade effect has been successfully used to prepare quantum states and realize quantum logic gates.Based on the Rydberg blockade effect and the theory of Lewis-Riesenfeld invariant,we propose a scheme to prepare an N-particle Greenberger-Horne-Zeilinger state and realize a controlled-not gate of multiple target atoms.The main contents are as follows:In Chapter 1 and Chapter 2,we briefly describe the theoretical basis related to our research work.In Chapter 1,we introduce the stimulated Raman adiabatic passage technology and controlled-not gate,and extend the controlled-not gate to multi-target qubit controlled-not gate.The blockade effect of Rydberg atoms is also briefly introduced.In Chapter 2,several common shortcut schemes are introduced.These schemes can accelerate the evolution of quantum states and make them stable in the adiabatic eigenstates.The above schemes provide a research basis for the scheme of designing a logic gate based on the Rydberg blockade effect and the shortcut to adiabatic passage method.In Chapter 3,we use the theory of Lewis-Riesenfeld invariant to accelerate the adiabatic evolution process of an N-particle Greenberger-Horne-Zeilinger state,which is based on the Rydberg atomic system.By comparing the adiabatic process with the acceleration scheme,we find that under the same Rydberg-Rydberg interaction strength,we can obtain the target state with higher fidelity and shorter time,so the acceleration scheme is more efficient.In Chapter 4,we design a scheme of a controlled-not gate for multiple target atoms by introducing additional auxiliary states,combining with the theory of Lewis-Riesenfeld invariant and Rydberg blockade effect.The population of each state is calculated by numerical simulation.We analyze the feasibility of the theoretical scheme and discuss the influence of atomic spontaneous emission and the feasibility of the experiment.The innovation of this paper is as follows:1.Compared with the adiabatic process,we use the shortcut to adiabatic passage to prepare an N-particle Greenberger-Horne-Zeilinger state.The simulation results show that the Rydberg-Rydberg interaction strength required by our acceleration scheme is smaller than that of the adiabatic process,and the acceleration scheme is less affected by atomic spontaneous emission than the adiabatic process.2.We propose a scheme for fast realization of a multiple-target-atom controlled-not gate.The shortcut scheme is applied to the evolution of the target atom,which greatly reduces the evolution time.The target state with high fidelity can be obtained by using this scheme,and the scheme has strong robustness to the influence of atomic spontaneous emission.