Enrico Fermi was a true pioneer in the field of calculating machines, and we have tangible examples right here at the CREF Museum. Today, the concept of a “computational machine” has expanded enormously, pushing major global industrial players like IBM, NTT, Huawei, and numerous startups to explore new frontiers, including quantum and photonic technologies.

This momentum is fueled by the end of Moore’s Law, the empirical rule that for decades guided the exponential growth of computing power in traditional semiconductors. In recent years, this growth has slowed sharply, reaching a plateau mainly due to inherent physical limitations.

This circumstance has put a spotlight on the search for new computational technologies. Added to this are recent concerns about the environmental impact of Artificial Intelligence. The algorithms that are shaping our society require exponentially growing computing resources: training a single AI can produce carbon emissions comparable to dozens of intercontinental flights. It is therefore crucial to develop technologies that are both more powerful than conventional processors and less energy-intensive, perhaps by operating at room temperature without the need for complex cooling systems.

In this context, photonics is emerging as the most promising technology. Recent studies demonstrate its ability to process enormous amounts of data in parallel using laser beams, which encode information through advanced modulation techniques. In the long term, the integration of quantum algorithms could revolutionize computing speed and pave the way for innovative cryptographic methods.

Photonic and quantum systems have the potential to solve optimization problems in polynomial time relative to the system’s size—a concept often called “Quantum Advantage.” This is precisely the goal that CREF is pursuing with its “Photonic Technologies and Artificial Intelligence” research line: to develop photonic quantum systems to accelerate computation, providing robust results in a classic format, not subject to decoherence, and therefore immediately interfaceable with traditional computers.

This ambitious work is structured along two parallel research lines: an experimental one, focused on the activities of the CREF Computational Photonics Laboratory, directed by Dr. Romolo Savo; and a theoretical one, focused on developing mathematical models and numerical simulations to test the large-scale efficiency of new combinatorial computing algorithms, under the guidance of Dr. Marcello Calvanese Strinati.

The experimental work at the Computational Photonics Laboratory is divided into two research lines that look at photonics and artificial intelligence (AI) technologies from complementary perspectives.

The first research direction—”Photonics for Machine Learning”—aims to create innovative computing machines based on photonic systems. These machines will be able to accelerate combinatorial computing for optimization problems (e.g., Ising machines) and to implement large-scale photonic neural networks. Both of these computing architectures are widely used in artificial intelligence, and their analog implementation based on light propagation has the potential to significantly reduce the computational resources, energy consumption, and environmental impact associated with the use of AI.

The second research direction—”Machine Learning for Photonics”—aims to use the powerful data processing techniques offered by machine learning to make some traditional optical material characterization techniques, such as interferometry and light scattering, more effective. The results obtained in this area will simplify the implementation protocols of optical techniques and extend their use to more complex situations and materials.

The theoretical work is also divided into two directions: “classical” and “quantum.” The classical analysis involves the formulation and study of new nonlinear dynamic models of a system of coupled parametric oscillators. The goal is to simulate the relaxation of a system of vector spins toward the minimum interaction energy between the spins. This system, called a “hyperspin machine,” is proposed with a dual purpose: (i) to find the minimum of the interaction energy between the simulated spins; and (ii) to implement new “dimensional annealing” schemes to increase the system’s ability to find the energy minimum of a binary spin system (Ising). The quantum analysis is based primarily on the formalism of open dissipative systems. The goal is to find non-trivial quantum effects in these oscillator models and to understand if they can be used to enhance classical computation.

Experimental Research: The Computational Photonics Laboratory

The lab has the infrastructure to develop prototypes of photonic computing machines and conduct related optical experiments. Our experimental methods are based on modulating laser light using spatial light modulators and on the interaction of light with complex photonic materials. The spatial modulation of the optical field’s phase allows us to encode millions of variables in a single light spot just a few millimeters across. The propagation of light through free space and through photonic materials with controlled properties enables the parallel processing of this enormous amount of data.

The materials of interest are complex and polycrystalline media engineered with photonic disorder and second-order nonlinearity. We use them as physical platforms for processing the information carried by light. The study and development of these materials are part of the lab’s research activities and are conducted through international collaborations (ETH Zurich, Université Sorbonne, TATA Institute Mumbai). The use of “ultrafast” pulsed laser sources (femtoseconds) is a key element of the lab’s research, as it allows us to use and study these materials in the optimal nonlinear regime.

The lab recently demonstrated the creation of the first large-scale “deep” photonic neural network. It’s based on the multiple scattering of laser pulses and the nonlinear generation of second harmonics in disordered polycrystalline samples fabricated by assembling nanocrystals of lithium niobate (LNO). A schematic of the experimental setup is shown in Fig. 1. This result was obtained within an international collaboration (Université Sorbonne, ETH Zurich, Tsinghua University Beijing) and was published in the prestigious journal Nature Computational Science. The result was also selected among the ten “breakthroughs” of 2024 by IEEE Photonics magazine.

Ongoing experimental activities include:

• The creation of a photonic Ising machine with multi-body interaction, based on the multiple scattering of laser pulses and nonlinear second-harmonic generation in disordered polycrystalline samples fabricated by assembling lithium niobate nanocrystals (LNO). We are experimenting with three types of optimization algorithms: i) sequential, ii) genetic, and iii) simulated annealing. This study is providing a better understanding of nonlinear phenomena in disordered photonic media. The creation of this machine will allow for the implementation of combinatorial optimization problems on a photonic platform that have previously been difficult to solve.

• The creation of a large-scale linear-regime Ising machine that uses continuous laser light and free-space propagation. It contains an innovative interferometric scheme that allows for the simultaneous monitoring of both the optical data processing plane (Fourier plane) and the optical data encoding plane (real phase plane). This photonic Ising machine is intended to be the first to be used for data classification in high-energy physics, specifically for classifying the detection coordinates of cosmic rays.

• The development of an innovative “phase unwrapping” technique for two-dimensional quadrant phase maps. It’s based on a classification procedure from convolutional artificial neural networks. The work involves creating a collection of interferometric images in the lab, consisting of tens of thousands of images, which are necessary to train the neural network. This technique is potentially applicable in numerous other fields, such as radar, acoustics, and telecommunications.

The lab also develops a numerical research line that uses simulations to investigate the creation of integrated photonic systems in lithium niobate for light manipulation through multiple scattering (in collaboration with ETH Zurich).

Theoretical Research

Given its recent idealization, the hyperspin machine is currently implemented numerically in two ways:

• By describing the dynamics of the parametric oscillators in continuous time as a system of numerous coupled differential equations (specifically, nonlinear Mathieu equations).

• By simulating the dynamics in discrete time through appropriate nonlinear maps, simulating at each time step the fundamental physical processes that govern the system’s dynamics (parametric amplification, intrinsic losses, coupling, and nonlinearity).

While the first approach demonstrates the general validity of the proposed system because the analytical model is not directly designed for a specific experimental realization, the second approach is particularly versatile and numerically efficient for proposing and, above all, testing specific experimental implementations of the hyperspin machine by simulating the fundamental processes mentioned above in the desired manner.

The analysis conducted so far by this theoretical activity on the hyperspin machine (and previously on Ising machines) has shown that the machine’s efficiency for the two purposes mentioned above depends in a non-trivial way on all the physical parameters that govern the system’s dynamics. We have observed that the hyperspin machine used as a minimizer of the interaction energy of vector spins shows an ability to converge to the global minimum that particularly depends on how much power (in terms of the pump field that realizes the parametric amplification) is input into the system. Similarly, it is known that an analogous problem is observed in Ising machines, where the system’s performance as an Ising model minimizer strongly depends on the physical parameters.

We have recently successfully tested the ability of the hyperspin machine with dimensional annealing to significantly increase the system’s performance as an Ising model minimizer and to reduce its dependence on various parameters (particularly the pump field) compared to the conventional Ising machine. The analysis was conducted by numerically implementing both the hyperspin machine and the Ising machine based on the formalism of nonlinear maps in discrete time, simulating two possible experimental implementations: optical and opto-electronic.

The question of how to limit the sensitivity of the hyperspin machine when used as a minimizer of vector spin models remains open. In the continuation of this analysis, we will study an extension of the parametric oscillator model used for the large-scale hyperspin machine with the aim of ensuring both greater accuracy of the system in converging toward the minimum energy of the simulated spin model and a robustness of the obtained results to variations in the system’s parameters.

Another aspect that the theoretical activity aims to study is the quantum effects in these systems. We recently proposed a study of quantum correlations (entanglement) by describing the dynamics of the quantum system with the formalism of open dissipative systems (Lindblad formalism). We numerically obtained the complete density matrix of the system using exact diagonalization methods. The analysis is limited to a few (two or three) oscillators due to the considerable numerical complexity of the problem. However, it successfully showed how the presence of the coupling between oscillators responsible for the formation of hyperspins gives rise to a strongly correlated state, even in parameter regimes where the system used as an Ising machine instead creates a semi-classical state. The implications of this result are currently under examination.