Theoretical Study Of Quantum Effect In Solid-State Circuits And Quantum Information Processing

As one of the candidate solutions, realization of quantum computation in the solid-state system has attracted much attention for its outstanding scalability as well as compat?ibility with modern experimental technologies. The solid-state realizations of quantumcomputation, to a certain extent, faces a major challenge of the coherence time. Namely,the coherence time must ensure that all the quantum gates can be performed completelybefore it decays. In recent years, people have witnessed the essential improvement ofsuperconducting device in its fairly long coherence time. Thus, it has become a hot topicof scientific research. Moreover, it is commonly known that the computation in super?conducting quantum systems is much the same as in the quantum optics system. Thecoupling of a dcSQUID, which serves as an artificial qubit with the superconductingtransmission resonating lines(TRLs), shares the same form of an atom coupled with theelectromagnetic ifelds. Superconducting system provides an ideal way to demonstratethe phenomenon of quantum optics.In this thesis, we proposed a model consisting of a series of charge qubits coupledwith two superconducting transition lines. By means of simplification and transforma?tion, we obtained the three-wave mixing Hamiltonian. We also analyzed the effects offour types of noises on the squeezing process by using of the master equation and quan?tum Monte Carlo methods. We have given the various factors that affect the squeezingprocess. We proposed an experimental scheme to detect the process of voltage squeezingusing modern microwave devices.In recent years, there has been significant progress in qudit computation theoriesand experiments. Superconducting phase qudit has been realized, which has been ap?plied to simulate spin systems. As the important quantum algorithms, Quantum FourierTransformation and phase estimation quantum algorithms have been extended to quditsystem. Here we have given the explicit forms of the high dimensional Quantum FourierTransformation and phase estimation, quantum algorithms, and analyzed the accuracyand the success rate. The advantage of the qudit systems is also analyzed by comparisonwith the qubit systems.Entanglement is an important property of quantum system, and it has played a keyrole in quantum information processing. In another work of this thesis, we have calcu? lated the averaged entropies of the linear cluster states. We have given the results forspecific systems, and derived analytical results for some special cases. Our results indi?cate that the averaged entropies of the cluster state are usually higher than those in theGHZ state and W state.