Date of Award

8-2022

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

Committee Chair(s)

Jia Zhao

Committee

Jia Zhao

Committee

Kevin Moon

Committee

Zilong Song

Committee

Hailei Wang

Abstract

Quantum computing has been an emerging technology in the past few decades. It utilizes the power of programmable quantum devices to perform computation, which can solve complex problems in a feasible time that is impossible with classical computers. Simulating quantum chemical systems using quantum computers is one of the most active research fields in quantum computing. However, due to the novelty of the technology and concept, most materials in the literature are not accessible for newbies in the field and sometimes can cause ambiguity for practitioners due to missing details.

This report provides a rigorous derivation of simulating quantum chemistry systems using quantum computers. The Hydrogen molecule is used as an example throughout the process to make it readable to a broader audience. Specifically, the ground state energies and the first-excited energies of the Hydrogen molecule, as well as the ground state energies of the Lithium Hydride molecule at different bond lengths under the governing of their corresponding Hamiltonians are explored through the Schrodinger’s equation, the Phase Estimation Algorithm (PEA), the second quantization, the Bravyi-Kitaev transformation (BKT), and the Hamiltonian establishment. Then, a quantum circuit is built from scratch based on the second-quantization and BKT Hamiltonian to demonstrate the process of quantum circuit derivation for quantum chemistry system. Lastly, Simulations on both the ground and excited state energies of the Hydrogen molecule and the ground state energies of the Lithium Hydride molecule are carried out based on the design of the circuits with Google’s Cirq quantum simulator. Finally, some quantitative and qualitative comparisons and analysis are conducted with the results.

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