Digital Quantum Simulation of Physical Systems on Noisy Intermediate-Scale Quantum Computers

Citation

Tan Teck Keng, Adrian (2023) Digital Quantum Simulation of Physical Systems on Noisy Intermediate-Scale Quantum Computers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/wget-ws64. https://resolver.caltech.edu/CaltechTHESIS:05072023-204014466

Abstract

Current quantum computers are characterized as having the order of 5-100 qubits, with limited connectivity restricting two-qubit operations to nearest neighbors, and with too much noise to achieve fault-tolerance. Such devices, called noisy intermediate-scale quantum (NISQ) devices, have been demonstrated to have sufficient coherent lifetime to perform interesting experiments motivated by quantum information sciences. This motivates the question of whether such devices can be utilized to study physical systems commonly encountered in condensed matter and quantum chemistry.

In this thesis, we address the open problem of identifying approaches to perform quantum simulations of physical systems on NISQ devices. We begin our study by considering the Hamiltonian ground state problem, a task routinely solved in numerical studies of materials and molecules. We provided a new quantum primitive, the quantum imaginary time evolution (QITE), that provides a practical approach to solve the Hamiltonian ground state problem. In addition, the QITE subroutine can be used in a Lanczos scheme to speed up convergence time.

Next, we consider the problem of performing finite temperature simulations and demonstrate how QITE can be used as a subroutine to develop scalable and feasible approaches to perform such calculations on a quantum computer. More specifically, we develop routines to obtain thermal averages by sampling minimally entangled thermal states, and also free energy by evaluating the partition function directly.

In our final study, we consider the study of topological states of matter, which do not fit within the Landau paradigm of local order parameters associated with symmetry breaking, and have been shown to exhibit unusual behavior. We show how a specific class of topological states of matter, the symmetry-protected topological states can be feasibly realized on present NISQ devices and their unusual behavior experimentally validated. Our study provides a benchmark of capabilities of state-of-the-art NISQ devices to study these interesting phases of matter.

Thesis Files