Protocols and applications for imperfect quantum devices

Thesis

Quantum computing is a rapidly advancing field that, if fully realized, promises to be revolutionary for applications including drug discovery, optimization, and cryptography. However, the challenges remaining to achieve this dream are considerable. Today's quantum computers (and those the foreseeable near future) are plagued by limited system sizes, decoherence, faulty operations, and a variety of other issues that have thus far inhibited quantum advantage on genuinely useful problems. While others pursue the ultimate goal of fully-fault-tolerant quantum computing, this thesis is about learning to live with these limitations, and to extract useful information from imperfect, noisy devices with no or limited quantum error correction. In this thesis, I introduce new algorithms that are resilient to these effects, study protocols that can best compensate for them, and probe the boundaries between quantum and classical systems.

This thesis spans three rather distinct topics in quantum technology: the use of imperfect quantum computers to study quantum systems; classically-efficient simulation of quantum devices; and quantum sensing in the presence of noise. I introduce new protocols and algorithms for each of these areas, and support them with both mathematical study and computer simulations. Broadly speaking, the contributions of this thesis are as follows. I introduce a new algorithm for resource-efficient estimation of excitation energies in quantum systems, studying its near-term applicability and scalability. I develop a new method for computing thermal properties of quantum systems on quantum computers, which appears particularly applicable to the early-fault-tolerant era, and expands upon previous approaches in both the resources required and the systems it can be applied to. I introduce a new classical simulation framework for variational quantum algorithms, expanding the domain of classically simulable problems in quantum computing, and demonstrate its application to archetypal problems in variational quantum computing and quantum machine learning. Finally, I compare protocols that compensate for the presence of noise in quantum sensing, showing that learning-based techniques are particularly promising.

Authors: Goh, ML

• DOI: 10.5287/ora-be4aajqzz
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: quantum algorithms; quantum simulation; tensor networks; quantum sensing; quantum computing; quantum error mitigation
• Subjects: Algorithms; Simulation methods; Metrology; Quantum computing