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Physics-inspired Computing and its Applications https://doi.org/10.17863/CAM.122633 Wang, Zhipeng 0000000176210416 Berloff, Natalia In this thesis, we explore the intersection of physics and computing, focusing on the development of novel computational paradigms inspired by physical systems. We first introduce how these physics-inspired computing methods can be applied to solve complex optimisation problems, by using the example of the Coherent Ising Machine (CIM), the gain-based XY machine, and the spatial-photonic Ising machine (SPIM), each of which demonstrating a unique approach to harnessing physical phenomena for computational tasks. After establishing the working principles of energy-based Ising machines, examplified by the SPIM, we investigate the current limitations of SPIMs, identifying hardware precision and coupling matrix rank of the optimisa- tion problem as key factors that impact the performance of SPIM. Bearing these constraints in mind, we propose the use of singular value decomposition and low rank approximation technique to expand the range of optimisation problems that can be handled by SPIM, and demonstrate its effectiveness through a practical ap- plication in portfolio optimisation in the financial sector. In addition, we investigate the use of constrained number partitioning (CNP) problem as a suitable benchmark for evaluating the performance of SPIMs, due to its computational complexity and low coupling matrix precision and rank requirements. We then shift our focus to dynamics-based computing, specifically the gain-based XY machine. The phase retrieval problem, which has wide ranging applications in imaging and signal pro- cessing, is reformulated as a XY Hamiltonian minimisation problem, which allowed it to be solved using the gain-based XY machine. It was then demonstrated nu- merically that the gain-based XY machine can solve the phase retrieval problem with a lower error than the state-of-art relaxed reflect-reflect (RRR) algorithm in the medium noise region, while having comparable performance in the high and low noise region, and this advantage persists when the scale of the problem is increased. It was further shown that the gain-based solver is able to solve phase retrieval problems constructed from both structured and unstructured initial data, indicat- ing its robustness and versatility. We demonstrate its practical utility by applying the gain-based solver to reconstruct a complex-valued three-dimensional vortex ring from real-valued intensity measurements, which could be realistically obtained in a Bose-Einstein condensate experiment. Finally, we explore the phenomenon of topological defect healing in optical networks, which will improve our fundamental understanding of the factors that determine the success or failure of dynamics-based optical networks in finding the global minimum of an optimisation problem. Focus- ing on one-dimensional rings and two-dimensional toroidal lattices, we show that under smoothness assumptions, the dynamics of optical networks admit solutions that contains transient zero-amplitude holes, which are known as instantons in one dimension, or rarefaction pulses in two dimensions. It is found that these transient zero-amplitude holes allow the system to remove initially present global phase wind- ings which are topologically protected, thereby allowing the system to converge to the true globally synchronised configuration corresponding to the global minimum of the XY Hamiltonian under the geometry we studied. From these findings, we iden- tify two key strategies to significantly enhance the probability of the optical network to reach the defect-free state - maintaining the system at a low effective injection rate just above bifurcation threshold, allowing the amplitude degrees of freedom to form zero-amplitude holes, and preparing the system with an initial condition with significant amplitude or phase inhomogeneities that can seed the formation of instantons and rarefaction pulses. We conclude the thesis by summarising the key findings and contributions of this work, and discussing potential future directions for research in physics-inspired computing. University of Cambridge 2025-07-04 Thesis Doctoral Doctor of Philosophy (PhD) eng Julian Schwinger Foundation Studentship; European HORIZON Pathfinder grant https://www.repository.cam.ac.uk/handle/1810/391521 https://www.repository.cam.ac.uk/bitstreams/0413241c-8d66-4c93-bd1a-866a0c4985c8/download 1499f739bb692427dcef6c0111261ce0 https://www.repository.cam.ac.uk/bitstreams/449fcd24-b5ae-4f71-8012-c00dbeee0a3e/download 87eda9de84448d1f82354d60eee3eb5f http://purl.org/NET/rdflicense/allrightsreserved physics physics-inspired computing analog computing Ising machine optimization