My research centres on two core questions:

• What makes a quantum system appear 'complex'?

and

• What can we do with this complexity?

It is often said that quantum systems are complex, and that this complexity underlies the revolutionary promises of quantum technologies. However, such statements are typically made informally; my research seeks to make them precise.

Indeed, simulating quantum dynamics on a classical computer bears a resource cost that grows exponentially with the size of the system; studying systems of more than a few particles quickly becomes intractable. Underpinning this is a fascinating duality: the very properties of quantum systems that make them appear complex to classical systems can be exploited to efficiently study complex classical systems with quantum devices. My research approaches this duality from both sides.

Under the broad umbrella of ‘quantum simulation’, I investigate how quantum technologies can be used to emulate and study the behaviour of complex systems -- such as weather and traffic -- and conversely, seek to understand which structures of quantum dynamics makes them appear complex to classical hardware. I am interested in the foundational aspects of this, such as the insight this provides into am 'intrinsic' computation within dynamical systems, as well as the practical applications for modelling complex systems. This includes adaptive systems ('agents'), such as autonomous vehicles, large language models, and artificial intelligences.

Moreover, such insight reveals powerful new approaches for improving our ability to simulate complex quantum systems with classical computers. A recent new direction of my research concerns the modelling of memoryful open quantum systems, i.e., those that interact strongly with their surroundings. With such environmental influence a major barrier to scaling quantum technologies, deeper understanding of its impact upon quantum systems and how we can control it is essential. This will enable us to mitigate against such environmental noise -- and potentially even harness it to our benefit.

I was awarded my undergraduate (2009-2013) and doctoral (2013-2016) degrees from the University of Oxford. Following this, I moved to Nanyang Technological University Singapore for a postdoctoral position, and in 2018 secured the prestigious Lee Kuan Yew Research Fellowship. In 2020 I moved back to the UK, where I held the Imperial College Borland Fellowship in Mathematics. Since October 2022 I have been based at the University of Manchester, where I hold a Dame Kathleen Ollerenshaw Fellowship in the Departments of Physics & Astronomy and Mathematics.

I am acting co-Director of the University's Centre for Quantum Science and Engineering, and Theme Lead for Information, Computation, and Physical Foundations. Within the Department of Physics & Astronomy, I am co-lead for Early Career Researchers.

I am also an editor at Quantum journal, a non-profit, open access journal for high-quality research across quantum science.

My team presently consists of myself and four PhD students. We are part of the broader Manchester Quantum Systems ('ManQS') theoretical physics group.

My research explores complex structure in quantum dynamics - and how this complexity can be harnessed - using tools from quantum information theory. 

Even the smallest of quantum systems can give rise to seemingly complex behaviours. While this can make such systems hard to model with classical computers, it presents a valuable opportunity - to use quantum technologies to efficiently model and simulate other complex systems. Recently, my research has focussed on how quantum computers can be used to simulate complex stochastic processes with a considerably smaller memory overhead than classically possible, and extending these results to the richer domain of adaptive agents - systems that modify their behaviour in response to environmental stimuli.

Potential project directions include:
• Exploring the interplay between quantum memory advantages and increased thermal efficiency, to e.g., design quantum protocols for extracting work from stochastic processes.
• Improving and extending the design of quantum-enhanced adaptive agents, and/or developing their potential areas of application.
• Using machine learning and related tools to enhance quantum memory advantages in stochastic simulation.
• Identifying and characterising the features of complex structure in quantum dynamics, and/or developing techniques for their efficient simulation.

The projects will be mostly analytical, with scope for a significant numerical/computational element. Students will develop a strong background in quantum information theory, and one or more of: open quantum systems; quantum stochastic processes; tensor networks; quantum thermodynamics; and quantum machine learning.

I lecture the core Y2 Physics module PHYS20101 Introduction to Quantum Mechanics.

I also typically supervise at least one MPhys project each year.

I hold FHEA status.