Research

Quantum algorithms

Quantum algorithms use superposition and interference to extract useful information from a quantum state. My work studies when this can reduce the cost of a computation, how to construct the necessary algorithms, and what their performance means for applications.

Hamiltonian simulation

Simulating quantum dynamics is a central application of quantum computing. My work includes algorithms for sparse Hamiltonians, simulation using truncated Taylor series, and generalised quantum signal processing. These methods also provide building blocks for other quantum algorithms.

Quantum chemistry and materials

I develop algorithms for simulating electronic structure, with attention to both asymptotic complexity and explicit quantum gate costs. This includes initial-state preparation using matrix product states, non-local pseudopotentials, spectral amplification, and the quantum fast multipole method.

Linear systems and differential equations

My work includes quantum linear-system solvers based on a discrete adiabatic theorem, algorithms for time-dependent differential equations, and nonlinear differential equations using higher-order methods and rescaling. The solution is typically encoded in a quantum state; the achievable advantage depends on the input, conditioning and information required from the output.

Quantum optics and information

Photon efficiency

Photon loss is a major limitation in optical quantum information processing. My research examines how single-photon efficiency changes under linear optical processing, including sources with coherence between their vacuum and single-photon components. Work with Alex Lvovsky established limits on improving single-photon sources.

Anyons and Bell inequalities

I have developed a proposal for simulating non-Abelian anyons using photons, and studied the assumptions needed to test Bell inequalities in the presence of loss. In particular, the usual fair-sampling assumption can be weakened.

Quantum metrology

Quantum metrology studies how quantum resources can improve measurement precision. My work combines fundamental bounds with explicit measurement protocols, especially for optical phase estimation and tracking.

Adaptive phase measurement

I pioneered Bayesian adaptive phase-measurement techniques that choose a feedback phase using the expected precision of subsequent measurements. I also developed methods for phase measurements using a local oscillator.

In collaboration with experimental groups, this work led to demonstrations of entanglement-free Heisenberg-limited phase estimation, non-adaptive phase estimation, and measurements using entangled photons.

Tracking a fluctuating phase

A changing phase introduces a trade-off between collecting more photons and following the signal’s motion. My research develops adaptive tracking methods using coherent and squeezed light, together with bounds on their precision. Experimental collaborations demonstrated adaptive quantum smoothing and quantum-enhanced optical phase tracking.

Measurement limits and laser coherence

I also study the fundamental limits of phase estimation and the coherence of laser beams, including the π-corrected Heisenberg limit and laser models with Heisenberg-limit coherence scaling.