Realization Of Deutsch-Jozsa Algorithm In Homonuclear Multispin Systems And Demonstration Of Simplified Quantum Process Tomography In Dephasing Process

Quantum computation (or Quantum information processing) has been intensively in-vestigated over past decades, since it is considered to be much more efficient than the clas-sical counterpart in solving some computational problems and simulating quantum systems. To realize quantum computation in nature, many physical systems and corresponding con-trol methods are proposed. In this dissertation, based on the liquid-state nuclear magnetic resonance (NMR) quantum computation, three main works are presented:1. we experimentally demonstrate the Deutsch-Jozsa (DJ) algorithm, in four-and five-qubit homonuclear spin systems by NMR technique, where we encode the one func-tion evaluation into a long shaped pulse with the application of gradient ascent algo-rithm. Compared with the early experiment for realizing DJ algorithm, our work tests kinds of non-trivial balanced functions for register number n>3, and the accumulat-ed errors due to gate imperfections and relaxation are dramatically reduced.2. quantum process tomography (QPT) is an essential tool to characterize dynamics of an open quantum system. Although standard QPT methods are hard to be scalable, simplified QPT approach is available if we have the prior knowledge that the system Hamiltonian commutes with the system-environment interaction Hamiltonian. Using a nuclear magnetic resonance (NMR) quantum simulator, we experimentally simulate dephasing channels to demonstrate the simplified QPT as well as the standard QPT method as a comparison. The experimental results agree well with our predictions which confirms the validity and better efficiency of the simplified QPT.3. Reduced resources for performing simulations of open quantum systems are desirable for experimentally understanding quantum information. In order to model the most general quantum operation on a d-dimensional system, a d2-dimensional environment is usually needed. As for quantum dephasing process, we find that this channel can be modeled by environment with the size of at most d dimensions. To justify this idea, we simulate a single qubit dephasing channel, with the system qubit under two envi-ronment qubit, by NMR quantum computation. Using the simplified QPT method to characterize this channel, we find’system-environment’model, in which the environ-ment is single-qubit, for the reconstruction of the channel. The experimental results imply that reducing resources for simulating open quantum systems is possible in the case of dephasing channel.Note that although our work is described in NMR quantum computation field, the pro-posed ideas, i.e., resorting to the numerical optimal method to find control parameters and the simplified QPT method, are theoretically not dependent on the specific physical appara-tus and can be applied to other quantum computation systems.