# π-Computing

## Physics-inspired Computing

## The need for new computing paradigms

The digital computing paradigm has been a cornerstone of economic growth for over five decades, marked by its exponential advancements. However, we now stand at a crossroads where the economic viability of further hardware enhancements is increasingly challenged. This juncture invites a pivotal shift, drawing inspiration from nature's fundamentally different and highly efficient approach to information processing, which starkly contrasts with our current binary, discrete-time computer systems.

Our research aligns with this emerging paradigm, investigating the use of physical systems with analog minimization capabilities. Such systems function with continuous variables and present a viable approach for tackling discrete combinatorial challenges. This includes quadratic binary minimization, a notable issue in the classical Ising minimization of discrete spins, where both theoretical proposals and experimental realizations of physics-based analog systems have been explored.

## Reimagining Computing – Using the Laws of Nature

Physics is remarkably succesful in explaining the behaviour of complex interacting systems. As most difficult real-world computing problems ultimately also arise from such complex interacting systems, it is no surprise that we turn to physics as an inspiration for new computing paradigms.

Physics-Inspired Computing encompasses numerous different topics. From developing new unconventional hardware such as analogue optical computers to developing novel optimisation algorithms – physics can serve as inspiration for all of them.

See below for an overview of the research performed in our group.

# Research Areas

## Optimisation

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.

## Neural Networks

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.

## Quantum Systems

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.

## AIM

The Analog Iterative Machine (AIM), built by our collaborators at Microsoft Research Cambridge, offers an alternative way of solving difficult problems by reimaging computer architecture in a fully analog domain. AIM is an optical machine that solves hard optimization problems at the speed of light — a space where state-of-the-art silicon solutions and even quantum computers fall short. All of this is done with commodity opto-electronic technologies that are low-cost and scalable.

Image from: D. Pierangeli, G. Marcucci, and C. Conti Phys. Rev. Lett. 122, 213902 https://doi.org/10.1103/PhysRevLett.122.213902

## Lasers

Coupled laser networks are a potential candidate as the physical platform to realise the analogue computing algorithms that we study. In a typical Ising or XY optimisation problem, a suitable physical system needs to be able to represent the time evolution of the phases of spins, and the time-invariant coupling strength between spins that encode the problem, and it has been found that suitably arranged spatial light modulators can be used in experiments to represent these quantities. Hence, analogue algorithms that are implementable by laser networks can potentially be realised in experiment, pushing the research frontier beyond just computer simulations.

## Polariton Condensates

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.

## Latest Developments

## New publications

### Analog Photonics Computing for Information Processing, Inference, and Optimization

Stroev, N., Berloff, N. G., Analog Photonics Computing for Information Processing, Inference, and Optimization. Adv Quantum Technol. 2023, 2300055. https://doi.org/10.1002/qute.202300055