Investigation of Quantum Computers for Quantum Simulation and Machine Learning

Citation

Kamakari, Hirsh (2024) Investigation of Quantum Computers for Quantum Simulation and Machine Learning. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rec5-4z30. https://resolver.caltech.edu/CaltechTHESIS:05282024-002413905

Abstract

The use of quantum mechanical phenomena for information processing has the potential to solve computational problems which are believed to be intractable for classical computers. Inspired by this potential, the last several decades has seen rapid development in both the theory and practice of quantum information processing. In this thesis, we explore three applications of quantum computing for the physical and computational sciences.

The first potential application is for the simulation of open quantum systems. We introduce two algorithms for the simulation of open quantum systems governed by a Lindblad equation. Based on adaptations of the quantum imaginary time evolution algorithm, these methods transform non-unitary open system evolution into unitary evolution which can be implemented on contemporary quantum hardware. We demonstrate these algorithms on IBM's quantum hardware via the simulation of the spontaneous emission of a two-level system and the dissipative transverse field Ising model.

Next, we explore efficient methods to probe measurement induced phase transitions using superconducting circuits. These phase transitions occur in monitored quantum systems as the measurement rate of randomized single qubit measurements increases. We overcome two exponential bottlenecks which limited the system sizes of previous experiments on superconducting circuits by employing a cross-entropy benchmarking protocol and Clifford based circuit compression techniques. We observed measurement induced phase transitions on systems of up to 22 physical qubits.

Finally, we switch our attention to machine learning, where we prove rigorous quantum advantages for adversarially robust classification. By constructing a learning task based on widely accepted cryptographic assumptions, we show a necessary condition for the utility of quantum computers for robust classification. In particular, we show that for the learning task we construct, any efficient classical learner cannot robustly classify better than chance, whereas a quantum learner can efficiently and robustly classify data with high accuracy.

Through these studies, we show that quantum computers have potential application in the physical and information sciences in both the near and long term.

Thesis Files