Description

This project will investigate the potential of quantum computing techniques to efficiently simulate quantum mechanics and quantum field theory phenomena and in particular explore the use of quantum computers and photonic systems as mathematical tools for investigating nonperturbative phenomena such as tunnelling.

Quantum field theory underlies our modern understanding of particle physics and condensed matter systems. However, performing dynamic simulations of quantum field theory on classical computers remains extremely challenging. Meanwhile, quantum technologies such as photonic circuits show great promise for developing new quantum computing hardware. Quantum computers have the potential to efficiently simulate other quantum systems. It has been shown that quantum annealers for example can successfully simulate quantum tunnelling phenomena, and can reproduce results for these processes that are in agreement with analytic approximations such as the WKB approximation. In principle this makes quantum simulation a tool for investigating non-perturbative phenomena, not only in simple quantum mechanical systems but in quantum field theory more generally. The aim of the project is to build on this work. This project will bring together the student's mathematics and physics knowledge and develop a full understanding of contemporary quantum computing and quantum algorithms, as well as non-perturbative phenomena and methods in field theory.

This project will investigate the potential of quantum computing techniques to efficiently simulate quantum field theory phenomena and in particular explore the use of quantum computers and photonic systems as mathematical tools for investigating nonperturbative field theory. You will learn core concepts in quantum field theory, quantum computing, and quantum algorithm design. Specific systems to model may include relativistic quantum mechanics and quantum tunnelling processes, and the possible use of boson sampling methods with photonic circuits. Other simulation methods for example utilizing quantum annealers or large circuit quantum gate computers will also be investigated.

What will I do in this project?

-- Review basics of quantum mechanics and eventually second quantization and key concepts in quantum field theory
-- Research quantum algorithms for simulating physical systems and processes
-- Implement simple quantum mechanics and simple field theory with existing quantum software libraries and develop new methods for gate quantum computers, quantum annealers or photonic devices.
-- Run simulations using quantum simulators and analyse performance
-- Compare with mathematical approximations.
-- Investigate algorithm improvements and extension to more complex quantum phenomena

Prerequisites

Mathematical Physics II and Quantum Mechanics III (or equivalent Physics module covering Quantum Mechanics) is required. Ability to programme in python to the level covered in first year Programming (other programming experience is fine if you didn't take the Programming I module in Maths).

Corequisites

Advanced QT would as a co-requisite would be beneficial but is not mandatory -- it may change the direction in which the project goes if you do not have it.

Resources

A good place to start to get a few details and pictures is Wikipedia-Quantum Annealing. There is an excellent introduction and practical starting point in the D-wave documentation D-Wave: what is quantum annealing? . For a recent paper on simulating quantum tunnelling see SAA+Spannowsky,Quantum-Field-Theoretic Simulation Platform for Observing the Fate of the False Vacuum . For a recent paper on simulating quantum tunnelling see SAA+Spannowsky+Williams, With a Little Help from Photons: Quantum Field Theory on Continuous-Variable Quantum Computers