The Application Of Quantum Zeno Dynamics In Quantum Computing

A quantum computer is a device for computation that makes direct use of quantummechanical phenomena to perform operations on data. The most fascinating feature of aquantum computer is that it would perform certain tasks faster than a classical computer,such as factoring a number and searching for data in an array. Since the concept of quan-tum computer was put forward, many national government and military funding agencieshave supported quantum computing research to develop quantum computers both in prac-tical and theoretical research. The quantum Zeno dynamics is di?erent from the generalquantum Zeno e?ect since the frequent measurements do not necessarily hinder the evo-lution of the quantum system, but the system can evolve away from the initial state via themeasurements , and a continuous coupling between the system of interested and the ap-paratus performing the observation can obtain the same physical e?ects as making use ofvon Neumann's projections and nonunitary dynamics. In this dissertation, by combiningthe cavity quantum electrodynamics, we mainly discuss the application of quantum Zenodynamics obtained by the continuous coupling in quantum computing.Based on the Zeno-like measurement, a theoretical method for generating three-and four-qubit decoherence-free states with respect to collective amplitude damping isproposed. The whole system is in a star configuration of a spin network and only considerthe nearest neighbor interaction between the outer spins and the central spin. The outerspin qubits consist of the decoherence-free state via measuring the state of central spinqubit at intervals of a finite time. The simulation results reveal that the fidelity approachesunity asymptotically, and the corresponding success probability reaches a stable value byincreasing the number of measurements. Furthermore, the decoherence-free states can beobtained within a small number of measurements after optimizing the interval time.Based on the quantum Zeno dynamics induced by the continuous coupling, a scal-able approach for generating multi-atom singlet states |S N? is proposed. The (N-1)-atomsinglet state |S N?1? and an ancillary atom are sent into the cavity, by adjusting the strengthbetween atoms and the classical fields till the Zeno requirements are satisfied, a finite Zenosubspace can be acquired and the N-atom singlet state |S N? is achieved after time selec-tion. Then a deterministic method for preparing arbitrary multi-atom symmetric Dickestates in cavity quantum electrodynamics via combining quantum Zeno dynamics with adiabatic passage is investigated theoretically which needs no measurements during thewhole operations. By quantitatively discussing the case of N = 4, it is shown that all thesestates are robust against both the loss of cavity and atomic spontaneous emission. Fur-thermore, the operating time is independent of both the number of atoms and excitations,which would reduce the complexity for achieving Dicke states in experimental operation.Based on the quantum Zeno dynamics induced by the continuous coupling, an ap-proach for directly implementing a controlled-not (CNOT) gate is put forward. Sincethe cavity and the classical fields drive di?erent level transitions, a closed subspace canbe obtained for numerical simulation and this CNOT gate is robust against cavity decay.Furthermore, an alternative approach for realizing the CNOT gate is also brought forwardwhich takes advantage of stimulated Raman adiabatic passage (STIRAP) with only sixpulses; thus it is insensitive to the atomic spontaneous emission. Then the concept ofdistributed quantum computation is introduced and the distributed CNOT gate is realized.The processχmatrices of the distributed CNOT gates for the ideal one and the practicalone are obtained by the quantum process tomography with overlap 96.52%. Finally aTo?oli gate is achieved via quantum Zeno dynamics in one step. This gate is a universalgate, which is not only valuable in complex quantum algorithms such as Shor's algorith-m and Grover's algorithm, but also has an immediate practical application as correctingoperation in quantum error correction.Based on the quantum Zeno dynamics induced by the continuous coupling, a 1→norbital state quantum cloning machine is implemented. This scheme utilizes the resonantinteraction between the superconducting quantum interference devices (SQUID) and thesuperconducting cavity. This kind of cloning belongs to the state-dependent cloning,which can e?ectively clone the quantum state on the Bloch Sphere with the same latitudebut di?erent longitudes. Thus the cloning machines for qubits in northern hemisphereand the southern hemisphere of the Bloch sphere are realized, respectively. The e?ectsof decoherence such as spontaneous emission and the loss of cavity are also discussedin virtue of master equation. The numerical simulation result reveals that the quantumcloning machine is especially robust against the cavity decay.