Quantum Computation,Control And Quantum Cor-relation In Many Body Systems

The quantum computation theory shows us a tempting future. However, there is still a quite long road towards the realization of a practical quantum computer. By the present time, we cannot yet produce qubits with both controllability and long enough coherent time. Besides, there is another important problem lack of well enough discussion, i.e., how to achieve better computation performance by arranging multi-qubit system in some ap-propriate way. In this thesis, we would review our previous research works focusing on the quantum computation, control and quantum correlation in multi-qubit systems, mainly including the following three parts,(1) We proposed a realizable scheme to implement a self-contained quantum refrigera-tor by Josephson qubits. This refrigerator system contains three qubits, playing the roles of the target to be cooled, the refrigerator and the heat engine respectively. By imposing proper resonant condition, indirectly we can get effective 3-body interaction from the orig-inal bipartite ones. Besides, we can provide the three qubits baths of different effective temperature, by inputing current noises of different strengths. After these preparations, the whole refrigerator could work well without other control fields.(2) We demonstrated how to do quantum computation in a array made from Josephson flux qubits by tunnelling operation. This is a system with topological order, whose ground space degeneracy is determined by the number of the punctures in the lattice, namely, the topology of the lattice. We showed how to encode logical qubits in the degenerated ground space. Proper external fields could drive the quasiparticles move along certain non-trivial paths in the lattice, and that completes the operation on logical qubits. In principle, we can do universal quantum computation in this system. (3) We studied the quantum correlation in topological quantum phase transition (TQPT), mainly on 1D and 2D systems. We found that in the 2D TQPT we studied, local quan-tum correlations completely vanish and only classical correlations exist. However, in the 1D TQPT system, the quantum correlations always keep nonzero values but are strongly suppressed. That implies the quantum correlations mainly hide globally inside topologi-cal order systems. We believe this distinguished property roots in the local transformation symmetry in TQPT systems.