Entangled States And Quantum Logical Gates In Cavity QED And Circuit QED

Quantum information science is one of the most exciting subjects in the past three decades, and many startling achievements have been achieved. The techniques for manipulating single atoms, photons, and electrons have became mature gradually, and the experimental tests for the fundamental principles of quantum information have also been realized. Quantum information, greatly changing the concept of information processing,shows a profound prospect for changing human life and production style and attracts more and more researchers’ attention. Two basic elements for quantum information processing are entangled states and quantum logical gates. This thesis investigates the physical implementations of the two elements in cavity quantum electrodynamics(Cavity QED)system and circuit QED system, aiming at providing theoretical support for the relevant researches.In the superconducting qubits and the microwave cavity resonantly coupling system,we propose schemes for achieving three-qubit GHZ state and two-qubit phase gate. Due to the resonant interaction, the proposed schemes can be realized in short time. The scheme is based on the Hamiltonian that one photon flips two qubit simultaneously, and does not involve any other auxiliary particles or energy levels. Under the unitary evolution, the schemes can be deterministically implemented with unit fidelity. This work can provide a new way for realizing entangled states and quantum gate using superconducting qubits in microwave cavity system. Considering the leakage of the cavity modes, we give the analytical expressions of the success probability and the fidelity of the schemes, which shows that the scheme can be achieved with higher probability and fidelity.Using the circuit QED system coupling superconducting qubits and the superconducting transmission line, we propose schemes for generating multi-qubit GHZ states and W states. Under the large detuning interaction between interferometer-type magnetic flux qubits and transmission line, we can obtain the Hamiltonian only involving atomic degree of freedom, which does not change the excited number of the system. We can construct GHZ states by introducing different phase shifts under the basic vectors with different excited number, and prepare W states by changing the populations of the different vectors in the space with the same excited number. Choosing different evolution time, the W states with the different parameters can be obtained. We analyze the influences of the large detuning approximation and decoherence on the present schemes, and the numerical results shows that these schemes can be achieved with high fidelity under the existing experimental parameters. Moreover, the operation time of these schemes does not increase with the number of the qubits, so combining with the mature integrated circuit technology of the circuit QED, these schemes have good scalability.We design a multi-qubit phase gate scheme in a new circuit QED system without rotating-wave approximation. The Hamiltonian without rotating-wave approximation is a newly developed model in circuit QED system, which usually has strong coupling strength and can be used to realize fast quantum information processing. We discuss two effective Hamiltonians under different conditions. The first one is the effective Hamiltonian obtained by perturbation approximation within the scope of the dispersion, and the other is the effective Hamiltonian at the special time point obtained by using the periodic evolution. Both of the two ways can obtain the XX coupling. Based on the effective XX coupling, we construct a multi-qubit phase gate with two steps. The multi-qubit phase gate can be achieved by performing multiple two-qubit phase gates with the same control bit and different target bits. For the reason of suppressing the decoherence of cavity modes, we perform numerical simulation with medial coupling strength. Under this coupling strength, the phase gate can be realized in 9.6 ns, and the time does not increase with the qubit number. Compared with the existing schemes, the operation time is very short in the present one. We numerically analyze the relation between the two methods to obtain the effective Hamiltonian and discuss the influence of the decoherence parameter fluctuations, which demonstrates the schemes are feasible under the existing experimental parameters. The final discussion about the scalability shows the schemes can be well extended.It is an ordinary strategy for preparing entangled states in current years to introduce special methods to control the adverse impact of the decoherence, where the feedback control based on measurement is a method relatively easy to implement. In the atomcavity QED system, we research the Bell states generation of two atoms dispersively coupling with a single-mode cavity under the feedback control of quantum jump. We first study the steady-state behavior of the system evolution without feedback, and find the steady state of the system can become maximum entangled mixed states without laser driven. When the feedback is performed, the entanglement of the system is greatly improved and the steady-state Bell states can be obtained. We discuss the influence of the detector efficiency on the steady state with and without laser driven, and clarify the effect of laser driven. We also discuss the influence of the different parameters’ variation, such as drive strength, feedback strength, driving detuning, and so on. The analysis about the physical device shows that atom-cavity QED system working in optical frequency is a suitable experimental system for our scheme.