In the quest for enhanced computing performance, there is a shift towards alternative hardware architectures and specialized devices. 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 can transmit information at extremely high speeds, 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 fiber 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.

Another promising direction involves utilizing spin glasses and their complex energy landscapes for computational purposes. Spin glasses are disordered magnetic systems characterized by frustrated interactions and a multitude of local minima in their energy landscape. By mapping computational problems onto the states of spin glass systems, it's possible to exploit their natural tendency to evolve towards lower energy configurations to find optimal or near-optimal solutions to hard optimization problems. Specialized hardware, such as analog spin glass processors or optical implementations of spin systems, can explore vast solution spaces in parallel. This approach leverages the intrinsic properties of spin glasses to perform computation through the system's dynamics, potentially offering speed and efficiency advantages over traditional architectures. However, practical implementation faces challenges, including precise control of spin interactions, readout of spin states, and mitigating thermal fluctuations that can affect computational accuracy.

Integrating spin glass models into computational frameworks not only provides an alternative hardware approach but also bridges concepts from physics and computer science, potentially leading to breakthroughs in solving complex problems. As research progresses, combining the advantages of photonic systems and spin glass dynamics might pave the way for innovative computing paradigms that overcome the limitations of current technologies.

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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