Quantum Computation And Quantum Information In Solid State Qubits: Many Qubits Manipulation

In quantum mechanics, quantum information is physical information that is held inthe state of a quantum system. The most popular unit of quantum information is thequbit, a two-level quantum system. However, unlike classical digital states which arediscrete, a two-state quantum system can actually be in a superposition of the two statesat any given time. The most interesting part of quantum computing research may wellbe the possibility to probe the boundary between the quantum and classical words. Themore macroscopic are the structures involved, the better. Superconducting quantumcircuits are the subject of intense research at present, in part because they have openedup a new area of fundamental science and in part because of their long-term potentialfor quantum computing. In this thesis, we will give a brief discussion ofsuperconductivity and two of the superconducting properties that underlie how qubitsoperate: flux quantization and Josephson tunnelling. And we will also review the threefundamental types of superconducting qubit, i.e., flux, charge and phase qubit, whichhave been currently studied.Entanglement of a quantum system has been intensively studied in a wide range ofresearch areas. Various systems have been considered to investigate the key role ofentanglement in quantum phenomena such as quantum phase transitions, many-bodyeffects, quantum information processing, and quantum transport. During the adiabaticand periodic time evolution of the system, i.e., the system Hamiltonian is varied slowlyand eventually brought back to its initial form, the entanglement has been shown toaffect the geometric phase of the system. For entangled bipartite systems, especially,geometric phases have been studied. Of particular interests is the geometric phase ofentanlged systems because of its use in the implementation of quantum informationprocessing.It is natural to ask how the interactions among the subsystems change thegeometric phase and entanglement of the composite system and what the relationbetween the Berry phase and the entanglement of the two qubit systems is. We considertwo interacting qubits to investigate the effects of interactions on the relations betweenthe Berry phases and entanglements for the eigenstates of the system. The XXZ-type ofexchange interaction will be employed to describe the interaction between two qubits.The effects of exchange-type interaction on the behaviors of the Berry phases and entanglements of two interacting qubits due to a slowly rotating external field arediscussed. The Berry phase and entanglement for the eigenstates of the systems areshown to be interrelated in a unique manner as the interaction strengths vary. We discussthe role of an anisotropic interaction in association with the relations between the Berryphases and quantum entanglements.Quantum gates are unitary operations used to describe the evolution of quantumstates and they lie at the heart of realization of quantum computing. Two-qubit gates aswell as single-qubit gates have been demonstrated in various types of quantum systems.A gate operation depending on a control qubit state can be performed, which is calledconditional gate operation, where the target states can be flipped for a control-NOT(CNOT) gate operation. In our study, a conditional quantum oscillation rather than aconditional gate operation is introduced by considering an effective interactingtwo-qubit Hamiltonian which can be adjusted within some system parameter ranges. Compared to the conventional proposals that are based on a combination of severalsteps of gate operations, manipulating conditional quantum oscillations enables us toperform an aimed gate operation in a single step. Thus, we investigate how conditionalquantum oscillations can be simultaneously manipulated to perform a controlled-gateoperation in a controllable and accurate manner.To clearly discuss an implementation ofconditional quantum oscillations to quantum gate operations, in this paper, we restrictourselves to a rotating wave approximation (RWA) in the presence of appliedtime-dependent fields, which allows us to capture an essential physics for controlledquantum gate operations based on conditional quantum oscillations. At resonantfrequencies, conditional Rabi and non-Rabi oscillations are shown to characterize thetime-dependent dynamics of the two qubit system. We discuss a frequency matchingcondition for achievable controlled-gate operations. By synchronizing the twooscillation frequencies on the matching condition, the CNOT gate operationperformance and operation time are shown to be controllable to obtain a very accurategate operation. Also, we perform a numerical calculation without any approximation.The numerical results show a well agreement with the analytic results. Further, it showsthat conditional quantum oscillations and their frequency synchronization are applicableto various quantum gate operations in solid-state multi-qubit systems such as Toffoliand Fredkin gates. Due to the quite strong qubit-qubit interactions in multiqubit setups,generating three-qubit gates directly is much faster than by universal gates. In this thesis,we will realize the three qubit Toffoli gate in the external field driven solid state system which is composed of three qubits with Ising interaction.