Macroscopic Quantum Phenomena Research Based On Superconducting Josephson Junction

As the rapid development of the information age, tranditional computer becomesharder and harder to cater for people’s requirement while dealing with and storing theinformation. Quantum computer has an unapproachable advantage comparaing totraditional computer, and is considered as the inexorable trend of information storageand information processing in the future. It has a lot of approaches to realize quantumcomputation, one of the most important schemes is superconducting quantumcomputation based on superconducting technology. Great development has taken placerecently for the superconducting qubit based on superconducting Josephson junction. Asa fully artificial solid-state quantum system, superconducting qubit has the advantagesof feasible operation, scalability and relative long decogerence time with respect tosome other solid-state qubit, and is considered as a possible candidate for the quantumcomputation. Besides, coupling with coplanar waveguide and some other two levelsystems, superconducting qubit could present lots of brand new quantum phenomenawhich have improtmant significance to the investigation of the basic principle ofquantum mechanics.Based on the superconducting qubit, this dissertation systematically elucidated thedevelopment history and the basic principal of superconducting qubit as well as thegreat progress in practical experiment. As is well known to all, one of the big obstaclesin quantum computation is the interaction between qubit and the environment whichwould lead to certain types of decoherence. Because of the limitation of shortdecoherence time in qubit, fast and exact gate manipulation in practical experiment isrequired. How to realize a fast and an exact quantum gate manipoulation in experimentbecomes a key problem. Non-adiabatic geometric phase gate manipulation has theadvantage of fast operation and anti-interference, is considered as a potential method torealize quanatum computation. This dissertation mainly studied the geometric phase inthe parameter space of superconducting flux qubit. The mainly result is as follow:(1) This dissertation proposed an experimental feasible scheme to implement thenon-adiabatic geometric phase gate manipulation in the parameter space of a flux qubitby controlling the microwave pulse added to the qubit. And an experimental feasiblepulse sequence is also proposed to implement geometric phase gate manipulation. The fidelity of geometric phase gate subjected to classic simulated noise is also calculated.By the simulation, this dissertation got: while the initial qubit state is the equalsuperposition of ground state and excited state, the geometric phase gate would have arelative high fidelity. This scheme also has some directive significance towards thepractical experiment.(2) The dissertation also proposed a scheme to implement non-adiabatic geometricphase and construct geometric phase gate in coupling flux qubits system. With respectto the coupling qubits system in dispersive regime, the dissertation calculated theeigenvalues and the corresponding eigenstates of coupling system by second-orderperturbation theory. Because of the perturbation, the effective dipolar interactionstrength between microwave and the coupling circuits has been decreased by a factorξ (ξ <1). Later on, by truncating the4-dimension Hilbert space of coupling flux quitssystem into a2-dimension sub Hilbert space, the dissertation presented how to constructa non-adiabatic geometric phase gate in detail. Finally, by the simulation, we also gotthe fidelity of geometric phase gate subjected to a given noise strength. The conclusiongot here is similar with part (1), that is while the initial state is equal superposition ofground state and first excited state, the phase gate would have a relative high fidelity.The conclusion of this thesis might be useful to practical experiment since itprovided a theoretical supports for the real experiment.