Much of my research is centred on ideas from the field of quantum computation. A quantum computer is a device that leverages quantum mechanics - the physical laws that govern the microscopic world - in order to solve computational problems that are thought to be impossible for ordinary computers. Since these devices are made up of many degrees of freedom, known as qubits, my aim is to understand the collective behaviour of many-qubit systems, with the aim to gain insight into the power of quantum computers, and how we might be able to use them to solve important problems in the future.

More broadly, I have worked on a number of topics that span quantum information, condensed matter physics, and statistical mechanics. Recently, I have been working on projects at the interface of all these disciplines.

Quantum mechanics tells us that the process of measuring an object inevitably disturbs the state of the system. Part of my research involves understanding how these measurement processes in a many-body quantum system can yield to different complex behavior.

Recently, together with Wen Wei Ho and Daniel Malz, I proved a conjecture that random constant-depth 2D quantum circuits followed by measurements can generate macroscopically long-ranged entangled states. As a result, we found strong evidence that these constant-depth circuits cannot be simulated by classical computers - thus demonstrating the potential power of quantum computers.

A key task in quantum computers is the problem of learning properties of quantum states. This is particularly important for the task of quantum simulation - using a quantum computer to mimic some other quantum system of interest, such as a chemical molecule, or a material.

I have developed new protocols for quantum state learning that can be implemented on present-day devices which have limited control, such as ultracold atomic gases in optical lattices. This allows one to infer physical properties that would otherwise be impossible to access.

As well as updating the state of the system, measurements also generate classical information in the form of a measurement outcome, which is intrinsically random. Adaptive quantum dynamics refers to processes where each operation performed depends on the outcomes of measurement that occurred before.

I have shown how measurement and feedback can be used to stabilize non-equilibrium phases of matter such as time crystals. I have also shown how adaptive quantum-classical processing can be used to learn about measurement-induced dynamics in a sample-efficient way.

The concept of topological phases of matter is an idea that originated in condensed matter physics, but was then shown to be related to important topics in quantum information, most prominently error correction. These are phases of matter - akin to familiar phases like solid, liquid, and gas - that fundamentally rely on quantum mechanical effects, like entanglement.

During my PhD, working with my supervisor Prof. Nigel Cooper, I conducted a number of studies of how topological phases of matter behave in scenarios away from equilibrium, and in open quantum systems. A particular achievement was to show that certain types of topological phase are qualitatively more fragile against the effects of non-equilibrium drive and noise than others.

In the domain of condensed matter physics, nonlinear spectroscopy is a newly accessible technique for probing the properties of materials by observing how they respond to external perturbations, specifically pulses of laser light. Together with Prof. Sid Parameswaran and Michele Fava, I showed that nonlinear spectroscopy can be used to detect collective excitations known as anyons. This can serve as a fingerprint signature of certain elusive topological phases of matter known as quantum spin liquids.