The Implementation Of C_k-NOT And C-NOT~k Quantum Gate Based On Unconventional Rydberg Pumping

Rydberg atoms not only have relatively long lifetimes,but also provides a long-range interaction mechanism between atoms,which are one of the most promising candidates for quantum computation and quantum simulation.Both the Rydberg blockade effect and the Rydberg antiblockade effect have been extensively researched in quantum information pro-cessing.On this basis,unconventional Rydberg pumping mechanism can provide a different effect from Rydberg blockadeand Rydberg antiblockade,i.e.,the atoms in the same ground states remain stable and the atoms in different ground states are excited resonantly.In this thesis,we mainly study the unconventional Rydberg pumping mechanism combining the ef-fective operator formalism of open quantum systems and Gaussian temporal modulation to implement scalable quantum logic gates with high fidelity.In the first work,we obtained an extended unconventional Rydberg pumping mechanism by applying classical fields of different frequencies and strengths to the transitions of atoms from ground state to Rydberg state.Based on this mechanism,we propose two schemes to implement controlled-not(CNOT)gates for neutral atoms.By adjusting the strength of the driving field between the target qubit,in the first scheme,we can achieve the fast implementation of two-qubit CNOT gate by resonant interactions.In the second scheme,the Rydberg state can be adiabatically eliminated by detuning interactions,the two-qubit CNOT gate is not influenced by spontaneous emission.By numerical simulation of the definition of state fidelity,the results show that the scheme of CNOT gate is robust in the neutral atomic system.In the second work,we apply a strong detuning field on the control atom and a weak resonant field on the target atom.Based on this driving mode,two-qubit CNOT gate can be directly extended to three-qubit C₂-NOT gate,i.e.,Toffoli gate.Taking into account the different atomic arrangement structure,by setting the same distance between the control atom and the target atom,the distance between control atoms can be unrestricted,a high-fidelity C₂-NOT gate can be obtained in the same operating time.Thus,our scheme can be directly extended to the multiqubit case.In the third work,we extend the single-target qubit CNOT gate based on detuning interactions to the two-target qubit CNOT gate,i.e.,C-NOT²gate.By Gaussian modulation of Rabi frequency of the target atom,the dynamics of the system is strictly confined to the ground manifold,this method exhibits more robustness against the fluctuation of system parameters such as operation time and environment noise.As a direct application of this C-NOT²gate,we prepare three-qubit Greenberger-Horne-Zeilinger(GHZ)for neutral atoms.The result shows that a high fidelity better than 99%can be obtained with the state-of-the-art experimental techniques.By extending the scheme to five qubits,under the impact of Gaussian temporal modulation,the fidelity of multiqubit GHZ state is more stable.