Measurement Based Quantum Computation

Quantum theory and computer science had experienced rapid progress in the 20^th century, the former of which changed our understanding towards the physical world and the latter changed people's life with each passing day. Quantum mechanics is a young subject and was founded in 1905. Having experienced a development of over 100 years, it is becoming more and more consummate, and a lot of achievements have been made. In the half centuries after the birth of the first computer, the computer technology has been developing with a great speed described by the Moore theorem. However, with the development of hardware, the volume of the elementary components of computer becomes smaller and smaller due to their high integration, which makes their quantum effects more and more prominent. Moreover, the heat over generated during the course of computation makes computer disabled. So there is great difficulty with classical computer and we must find other computation modes to resolve this problem. In this situation comes the quantum computer. Quantum computer is the combination of quantum mechanics and computer science, in which classical bits are replaced by quantum bit (qubit), the information is encoded in quantum states and quantum computation is realized through the evolvement of some certain quantum states. Quantum computer is promising for the great speed of its parallel computation and quantum simulation. However, there is a lot of difficulty in the realization of universal quantum computer. This paper is mainly about a class of quantum computation schemes: measurement-based quantum computation and the progress that has been made is as follows:After the research on the so-called one-way quantum computer scheme proposed by Briegel and Rossendorf, a new scheme is presented, which can be used in a wider range of physical systems. In 2005, Duan et al. presented a scheme that can realize efficient quantum computation on cluster with probabilistic quantum gates. This scheme, combining the idea from quantum repeater and the cluster state approach to computation, resolves the inefficiency problem caused by the system noise, which means that 2D lattice-like cluster state can be prepared efficiently no matter how small the success probability of the gate operation is. In Duan et al.'s scheme, all the preparation is parallel and the ruined qubits caused by failed operations are discarded and replaced by new ones. So it can not be used in some physical systems in which the positions of qubits are fixed, for example, quantum dot. In this paper, the author resolve the problem and make the scheme adapt more experimental systems with the aid of the ancilla qubits prepared on the third dimension.A scheme to efficiently prepare 3D or high-dimensional cluster state is presented. In fact, there is always noise in experimental systems. If we make the preparation in a normal way, the operation time T will increase exponentially with the qubit number n. Using the scheme presented in this paper, which combines quantum repeater, the main properties of the cluster state and the idea from Duan et al.'s scheme, we can realize efficient preparation of high-dimensional cluster state no matter how small the success probability of the gate operation is. The 3D cube-like cluster state can save a lot of experiment space and the computation power is enhanced.A class of unlockable bound entangled states and their applications are stutied. No pure entanglement can be distilled from this class of states by local quantum operations and classical communications. However, if certain parties group together, they become distillable. Although they are bound entangled states, they could be used to achieve some non-trivial tasks, such as quantum secret sharing.