The Research Of Measurement Based Quantum Computation And Algorithm

The combination of quantum mechanics and computer science has produced a new cross disciplinary—quantum computation and quantum information. Quantum computing has a tremendous speed advantage in the aspects of parallel computation and quantum simulation, so it has a very attractive application prospect.In this thesis, i mainly study a kind of computing model of quantum computation—measurement based quantum computation(MQC model). In MQC model, the main process is usually to start with a given fixed entangled state of many qubits, followed by a series of quantum measurement in the selected basis. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation. Two principal schemes of measurement based computation are teleportation quantum computation(TQC) and one-way quantum computer(1WQC). TQC model is based on the idea of teleportation and computes by applying rotated Bell measurements,and 1WQC model computes by applying a sequence of single qubit measurements on a cluster state.In this thesis, based on the previous studies, the TQC model and 1WQC model were further studied. The similarities and differences between TQC model and 1WQC model are given, and the universal quantum computation is realized by using TQC model and1 WQC model. The main contents and results are as follows: For TQC model, this thesis not only describes the realization of universal single qubit gate, but also proposes measurement strategies of continuous single qubit gates, and prove it in detail. This thesis also promote the TQC model by promoting Bell measurement to general measurement,and the analysis of the expansion of the Bell measurement has the function of quantum encryption. For the 1WQC model, this thesis firstly presents the method to realize universal single qubit gate by using 5 qubits and 4 times single qubit measurements. And on the basis of research and analysis, then puts forward a method to realize universal single qubit gate by using 4 qubits and 3 times single qubit measurements. At the same time,this thesis also considers a sequence of n single qubit gates, realizes n quantum gates by using 3n + 1 qubits and 3n times single qubit measurements, proposes measurement strategies and additional Pauli matrices in the form of theorem, and prove it with mathematical induction in detail. This thesis also discusses general entanglement, through the analysis of that due to the symmetric and Hermitian of CZ gate, so it is necessary to use CZ gates to generate the entanglement between adjacent qubits in 1WQC model. Finally,by studying the Shor algorithm and the Grover algorithm, the Shor algorithm and the Grover algorithm based on measurement model are also proposed.