Quantum simulation and a study of entanglement and its application in quantum teleportation
Abstract
This thesis contains four projects: entanglement and quantum phase transition in one-dimensional quantum dots system; entanglement and electron correlation in molecular systems; quantum teleportation in one-dimensional quantum dots system and simulation of molecular systems on a quantum computer. Chapter 1 presents a general introduction to quantum computing. A brief history and motivation for quantum computing is introduced. In Chapter 2, we studied the entanglement of an array of quantum dots system modeled by one-dimensional Hubbard Hamiltonian and the relation between quantum entanglement and quantum phase transition. In Chapter 3, entanglement in molecular systems is studied. It is proved that the full configuration interaction (FCI) wave function violates Bell’s inequality, thus it is entangled; while the Hartree-Fock (HF) wave function does not violate Bell’s inequality, so it is unentangled. Based on this, we studied the relation between quantum entanglement and electron correlation in molecular systems. We suggested that quantum entanglement might be used as an alternative way to measure electron correlation in molecular systems. The application of entanglement in an array of quantum dots system in quantum teleportation is studied in Chapter 4. We showed that the space-spin entanglement in the quantum dots system can be filtered to obtain pure spin (space) entanglement, and it can be used in quantum teleportation. We also showed that by selecting appropriate Hamiltonian for the C-NOT gate, the spin-based information can be transformed into charge-based information. The pulse sequence for realizing the C-NOT operation is given. In Chapter 5, we studied the simulation of molecular systems on a quantum computer. We proposed a quantum algorithm to solve the Schrödinger equation using the basis set method based on the multi-configuration self-consistent (MCSCF) wave function. By using this algorithm, the potential energy surfaces of molecules, even some complicated regions, can be studied more efficiently than if the simpler HF wave function was employed. This algorithm can give high success probability, almost deterministic results for ground state and excited states. A small increase in the number of configuration state functions in the MCSCF wave function can dramatically increase the success probability of the quantum algorithm. A multi-reference configuration interaction approach is suggested for the treatment of larger systems. We generalized this method to the finite element method and simulated a quantum system of one particle in Yukawa potential. We showed that numerical methods for solving differential equations can be implemented efficiently on a quantum computer.
Degree
Ph.D.
Advisors
Kais, Purdue University.
Subject Area
Physical chemistry
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