Quantum algorithms from the near to future term

Thesis

Many important physical and mathematical problems are difficult to solve on classical computers, resulting in difficulty in finding new advanced materials, simulating quantum field theories and solving large combinatorial optimisation tasks. Quantum computers have shown great promise in being able to solve these (and many other) problems faster than their classical counterparts, and therefore should be thoroughly investigated as a significant tool for enabling the acceleration of scientific progress.

This work develops methods to tackle several problems across the spectrum of quantum algorithms, providing methods suitable for the near-term hardware, to the future where large fault-tolerant quantum computers exist. Therefore, the works in this thesis range from efficiently making use of limited quantum hardware to taking advantage of hardware benefits (e.g. excess qubits) as quantum computation advances.

Covered topics include: an alternative paradigm for the optimisation of variational circuits and quantum neural networks; techniques for improving energy estimation of quantum states through the collection and processing of large amounts of randomised measurement data; the use of entanglement in guiding the automatic discovery of quantum circuits; investigating the role of symmetries in adiabatic state preparation of molecules and the large scale parallelisation of a common fault-tolerant subroutine, potentially producing large runtime speed-ups for the simulation of chemistry on quantum computers.

Although there are many challenges remaining from both hardware and algorithms perspectives before the large-scale utility of quantum computers can be demonstrated, the contributions of this work make steps towards the efficient utilisation of quantum hardware that will be available in the coming years.

Authors: Boyd, G

• DOI: 10.5287/ora-ob9aar5jj
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English