There is a shift towards alternative hardware architectures and specialized devices in the quest for enhanced computing performance. Among these, universal quantum computing emerges as a solution to reduce algorithmic complexity in challenging tasks by leveraging entangled states. An alternative strategy involves transitioning from electron-based to photon-based systems within classical or quantum-coherent optical computing. The rationale for this shift is evident: photons travel at light speed, generate minimal heat, enable high-density configurations, and can effectively interact with matter to harness nonlinear effects. Optical technologies have become ubiquitous, evidenced by their presence in everyday applications like fibre optic communications and optical disc readers. Yet, a significant challenge in integrating photonics with CMOS architecture is the energy-intensive and time-consuming conversion of photons to electrons, posing a substantial bottleneck in hybrid systems.

Physics-inspired optimisation leverages physical systems' properties, particularly in optics and photonics, to tackle a wide array of complex optimisation problems, offering new possibilities beyond the capabilities of traditional computing methods. Physics-inspired optimisation encompasses a broad spectrum of solutions for various optimisation problems, including linear and nonlinear tasks in binary, integer, real, or complex variables, both with and without constraints. This extensive applicability enables its use across diverse sectors such as social sciences, finance, telecommunications, and biological and chemical industries.

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Optics and coherent light-matter systems have the potential to implement artificial neural networks (ANNs), a technology increasingly recognized for its inherent parallelism and low energy consumption, making it a suitable candidate for industrial and fundamental applications. While ANNs are predominantly electronic-based, the shift towards photonic neural networks is gaining momentum. In photonic ANNs, mathematical operations are mapped onto optical propagation characteristics, manipulated by programmable linear optics and nonlinearity. Synaptic weights in these networks are scalar and represent the pairwise connections between neurons, with the layout of interconnections mirroring matrix-vector operations where neuron inputs are the dot products of outputs from connected neurons with assigned weights.

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Quantum systems, with their inherent properties of superposition and entanglement, offer a revolutionary perspective in computational optimization and neural networks. The exploration of quantum optimizers and neural networks that emulate quantum properties is at the forefront of current research, blending the boundaries between classical computing paradigms and quantum mechanics.

Quantum optimizers harness the unique capabilities of quantum states to explore complex problem spaces more efficiently than classical systems. Quantum annealing, for example, exploits quantum tunnelling to traverse energy landscapes, potentially finding global minima more effectively in optimization tasks. This approach is particularly advantageous for solving problems that are intractable for traditional computers, such as specific combinatorial optimization and machine learning tasks.

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Arrays of polariton condensates hold considerable promise for developing ultrafast analog simulators proficient in modeling spin ordering, synchronization in lattices, neural networks, and NP-hard optimization problem solvers. The key lies in the Gain-Dissipative mechanism, which rapidly drives the system towards the global minimum of the spin-Hamiltonian increasing gain from below, and then sustain achieved final state long enough to allow experimental measurements. This promising class of analog simulators is devoid of disadvantages related to the scaling difficulties, can operate effectively at room temperatures, and can be implemented within relatively short time scales using various experimental platforms with tunable properties. These features make these systems one of the most intriguing platforms for the development of a new generation of non von-Neuman architectures.

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