Images are rich in data of significant economic and social value, and over the past decade, they have become fundamental sources of information in many disciplines (e.g., medicine, biology, agriculture, defence, earth sciences, and non-destructive testing). These disciplines now drive the development of sophisticated and specialised imaging devices. Such devices tightly combine two forms of innovation to deliver state-of-the-art performance: 1) sophisticated instrumentation and sensors that push technology and physics to the limits, and 2) highly advanced computational imaging (CI) methods that carefully analyse the generated raw data to produce sharp images with fine detail. This proposal focuses on CI methodology for quantum-enhanced imaging, a new imaging paradigm that seeks to exploit the quantum nature of light to go far beyond what is possible in classical optics in terms of spatial and temporal resolution and dynamic range. This transformative approach is poised to dramatically advance imaging technologies and generate great social and economic impact. To make sure that the UK is at the forefront of this strategic technological developments, the UK government created the Quantum Enhanced Imaging Hub (QUANTIC) in 2014 as part of the UK National Quantum Technology Programme, which was renewed this year. QUANTIC has developed impressive new sensors for extreme imaging conditions. However, these advances in sensor technology have not been matched by progress in CI methodology, gravely jeopardizing the impact of these promising technologies. The aim of this proposal is to develop CI methodology specifically designed for solving quantum-enhanced imaging problems in which very few photons are observed (i.e., low-photon and single-photon imaging problems). Our methods will be formulated in the Bayesian statistical framework, which is particularly appropriate for solving these challenging imaging problems because: 1) it enables the use of sophisticated statistical models to accurately describe the underlying physics, 2) it allows the automatic calibration of models, and 3) it provides tools to quantify the uncertainty in the solutions delivered. At present, the benefits and superior performance of Bayesian statistical CI methods is obtained at the expense of a prohibitively high computational cost. We plan to significantly accelerate Bayesian solutions for quantum-enhanced imaging problems by developing specialised computation methods that combine and extend ideas from different areas of applied mathematics, computational statistics, and artificial intelligence. We believe that the availability of fast Bayesian computation methods will unlock the potential of these promising quantum-enhanced imaging technologies and lead to their wide adoption in science and engineering, generating generate great social and economic benefit through an impact on medicine, biology, agriculture, defence, earth sciences, and non-destructive testing. In order to guarantee this impact, during the project, we will apply the proposed methods to three important quantum-enhanced imaging problems (low-photon multispectral single-pixel imaging, high-resolution PGET, and single-photon 3D LIDAR with array sensors). These applications will be investigated in collaboration with world-leading experts who will provide data and training, and help disseminate the research outputs. To maximise the impact of our work, we will also develop open-source software - with documentation and demonstrations - that we will share online and use in outreach activities aimed at informing the public about STEM research and inspiring young people to pursue STEM careers. This project will also help train the next generation of top-tier talent in AI and quantum technology.

Dimensionality is hugely important in low-temperature physics, the study of materials and the behaviour of electrons and other excitations in solid crystals. The underlying mathematics and the resulting observed behaviour of a material or system is hugely and fundamentally different and exotic if its character becomes two-dimensional rather than the familiar 3D. Even more fascinating and elusive is the fuzzy halfway ground of how a system behaves as it is pushed from one regime to the other - '2.5D'. A nascent revolution in alternatives to silicon-based electronics is increasingly turning to the physics of 2D materials to design new devices to overcome the challenges of ever-increasing miniaturisation and an ever-mounting drive to become more energy efficient. 2D layered crystals have unique advantages in this regard, as they can be cleanly and easily thinned down to single layers of atoms (as with the famous example of graphene), then stacked together in nigh-unlimited complex configurations to combine their exotic properties. To design and use these systems at an application level, it is essential that the underlying physics, and with it both the limitations and possibilities intrinsic to the materials are fundamentally understood and tested. Furthermore, this research can inform potential new avenues to explore and the synthesis of new designer materials to fulfil established criteria. A large volume of recent work on low-dimensional physics has focused on thickness control, to tune towards the `true 2D' limit of the atomic monolayer. A complementary approach is to tune the interactions from 2D to 3D by applying hydrostatic pressure - an extremely clean and powerful tuning parameter in a van-der-Waals (vdW) material. These materials are formed of strongly-bonded flat planes of atoms, linked only by the extremely weak van-der-Waals chemical bond - akin to static electric attraction. Applying pressure to such a system overwhelmingly has the effect of pushing the crystal planes together, strengthening bonds between them and allowing ever-increasing crosstalk. This will often have profound effects on the conductivity and magnetism seen in the system, including the discovery of exotic new states of matter. I will use extremes of low temperature, high pressure, magnetic and electric fields to search for new functional and multifunctional quantum materials and tune existing systems into novel states, focussing on fundamental properties of transport and of magnetic and charge order in 2D materials. I will focus on fundamental properties of transport and magnetism in low-dimensional van-der-Waals materials, and then to nanoscale devices built from stacking individual atomic layers of different 2D materials together. Extreme-conditions tuning of these nanodevices is a completely new and exciting research direction that brings together two very different fields of research with essentially no overlap - my unique background across these two areas, and quantum computing, will allow me to build a new interdisciplinary programme to explore exciting new physics. These devices additionally harbour great potential for new technologies as well as blue-skies science interest. I am partnering with industry, and academic collaborators in electrical engineering, chemistry and materials science, to explore pathways to practical applications of the new materials, behaviours and architectures to be discovered. Potential uses are in new times of electronics and memory such as spintronics or low-power transistors, flexible electronics and precision sensors. I will also look to harness the exotic 'topological' properties of new 2D materials to build fault-tolerant new qubits for quantum computing, drawing on my expertise and contacts in this field.