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PhD scholarship: Advanced Monte Carlo simulation of quantum fields: taking worldline sampling beyond the diffusive regime

University of Warwick – School of Engineering

Qualification aim: Doctor of Philosophy in Engineering (PhD)

Start date: 30 September 2024

Funding duration: 3.5 years

Supervisor: Dr Michael Faulkner (Warwick Centre for Predictive Modelling)

External project partner: Dr James Edwards (Centre for Mathematical Sciences, University of Plymouth)

Project summary:

Recent advances in computational quantum field theory have led to non-perturbative approaches to predicting scattering amplitudes and correlation functions in quantum mechanics. This holds much promise for transforming elegant quantum field theories into the genuine predictive modelling of quantum systems, but the diffusive dynamics of industry-standard simulation algorithms generate highly correlated samples of the target distribution. This project will develop state-of-the-art simulation algorithms whose ballistic-style superdiffusive dynamics drive the system through its state space – rapidly generating samples with very low autocorrelation and paving the way to high-quality quantum predictions.


The worldline-numerics approach to simulating quantum field theories has created many opportunities for generating high-quality predictions of scattering amplitudes and correlation functions in quantum mechanics. It circumvents the convergence issues associated with standard perturbative methods by instead aiming to draw a representative sample of quantum fields at each point in an array of fixed times. Industry-standard approaches use the Metropolis Monte Carlo technique to sample the field values at each fixed time, but this is a significant barrier to high-quality predictions because its diffusive dynamics generate highly autocorrelated Markov chains – making it a real challenge to generate independent samples of the target distribution.

Recent advances in statistical physics and data science have developed, however, a new class of deterministic Markovian sampling algorithms called piecewise deterministic Markov processes (PDMPs). In contrast with the diffusive dynamics of the Metropolis approach, these algorithms drive the system deterministically through the state space, rapidly generating independent samples of the target distribution. This project therefore aims to develop a PDMP approach for the worldline sampling problem. The rapid generation of highly decorrelated samples of the worldline distribution will lead to high-quality predictions of scattering amplitudes and correlation functions, opening up numerous avenues for future developments and applications.


The studentship is supported for 3.5 years and includes full ‘home’ tuition fees plus a UKRI-standardised stipend of £19,237 per annum, which fully funds those applicants eligible for home fees with relevant qualifications.


Applicants should have a first or a strong upper second-class honours degree in an appropriate subject, and preferably a relevant Master’s qualification or comparable research experience. Experience with programming and numerical approaches to statistical physics, quantum mechanics and/or quantum field theory is desirable. Prior exposure to the worldline formalism of QFT and/or PDMPs is favourable, as the project extends the worldline Monte Carlo technique to PDMP sampling algorithms.

How to apply:

Candidates should submit an expression of interest by sending a CV and supporting statement outlining their skills and interests in this research area to If this initial application succeeds, we invite you to apply for study formally. All candidates must fulfil the University of Warwick entry criteria and obtain an unconditional offer before commencing enrolment. Informal enquiries to are welcome.

Application form 'Course search':

Department: School of Engineering

Academic Year: 2024/25

Type of Course: Postgraduate Research

  • Engineering (MPhil/PhD) (P-H1Q2)

In the application form funding section, enter: Source: Monte Carlo

The University of Warwick provides an inclusive working and learning environment, recognising and respecting every individual’s differences. We welcome applications from individuals who identify with any of the protected characteristics defined by the Equality Act 2010.

    This project brings together expertise from the Warwick Centre for Predictive Modelling and the Centre for Mathematical Sciences at the University of Plymouth. Interaction with the taught modules of Warwick’s HeySys CDT — as well as with world-leading PDMP collaborators in Warwick Statistics — will provide the applicant with the advanced skills required to develop the necessary PDMP algorithms, allowing us to tackle this exciting research project. Large-scale simulations will be performed on Warwick’s high-performance-computing infrastructure, and the applicant will develop a high level of research software engineering skills over the course of the project. There is also the potential for travel to visit external project partners, including at the University of Plymouth