UBC Undergraduate Research

The Use of Matrix Product State Representations in Simulating Many Body Quantum Systems Low, Matthew


The classical simulation of many body quantum systems has long been of interest to both condensed matter and quantum information theorists. The use of matrix product state representations of the wavefunction allows suitable approximations to be made that permit quantum simulations to be performed in polynomial time rather than exponential in the size of the system. The numerical methods are based on a minimization algorithm that can be used to nd the ground state and rst excited state energies and their respective matrix product states. Using the matrix product states, other quantities such as magnetization and correlation can also be computed. In this thesis, the theory and numerical techniques necessary for these simulations are studied and applied to the one dimesional Ising model in a transverse eld. The results of the model are compared to the analytical solution and analyzed in depth.

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