Research On Quantum Simulation And Entanglement Witness

The research field of quantum information and quantum computation, an interdisciplinary field which involves quantum mechanics, computer science and the theory of information, has attracted more and more interests. Recent years have witnessed the very fast progress in both theory and experiments.One of the most important applications of quantum information processing is quantum simulation, which was first proposed by R. Feynman in 1980s and demonstrated at the beginning of this century. The central idea of quantum simulation is that it is impossible for a classic computer to simulate the evolution of a quantum system, which can be only simulated by another quantum system. One of the key problems of quantum simulation is how to map the parameters in the two quantum systems before and after the simulation. This problem is explored in chap.2, where we will show that a novel simulation protocol based on spin analogy and submatrix diagonalization can be used to solve the reduced BCS Hamiltonian. The further application of our simulation protocol will give the energy gap, which is consistent with result obtained by the usual energy gap equation. Experimental realization of our protocol has been exploited by means of 2-qubit NMR system recently, where the reduced BCS Hamiltonian was simulated.Another important application of quantum information processing is to investigate entanglement properties in solid state systems. Recently entanglement has been explored as a new tool to enhance our understanding of the property of quantum many-body systems. It is difficult to investigate the entanglement property of a solid system directly, since there are so many particles in it. However, it has been shown that entanglement properties of many body system is closely related to some macroscopic measurable quantities, called entanglement witness, which allow for exploiting the entanglement properties by measuring macroscopic...