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This roadmap consolidates recent advances while exploring emerging applications, reflecting the remarkable diversity of hardware platforms, neuromorphic concepts, and implementation philosophies reported in the field. It emphasizes the critical role of cross-disciplinary collaboration in this rapidly evolving field.

Variational quantum algorithms are hybrid quantum-classical approaches extensively studied for their potential to leverage near-term quantum hardware for computational advantages. In this work, we successfully execute two variational quantum algorithms on a silicon photonic integrated circuit at room temperature: a variational quantum eigensolver for the Hydrogen molecule and a variational quantum factorization for semi-prime numbers. In our reconfigurable silicon photonic circuit, four identical spontaneous-four-wave-mixing-based integrated photon pair sources are used to prepare two path-entangled ququarts, whose correlation gives rise to the resource for generic trial states' preparation. This marks a first demonstration of variational quantum algorithms on a photonic quantum simulator with integrated photon pair sources., Comment: 42 pages, 13 figures

Photonic neuromorphic computing may offer promising applications for a broad range of photonic sensors, including optical fiber sensors, to enhance their functionality while avoiding loss of information, energy consumption, and latency due to optical-electrical conversion. However, time-dependent sensor signals usually exhibit much slower timescales than photonic processors, which also generally lack energy-efficient long-term memory. To address this, we experimentally demonstrate a first implementation of physical reservoir computing with non-fading memory for multi-timescale signal processing. This is based on a fully passive network of 64 coupled silicon microring resonators. Our compact photonic reservoir is capable of hosting energy-efficient nonlinear dynamics and multistability. It can process and retain input signal information for an extended duration, at least tens of microseconds. Our reservoir computing system can learn to infer the timing of a single input pulse and the spike rate of an input spike train, even after a relatively long period following the end of the input excitation. We demonstrate this operation at two different timescales, with approximately a factor of 5 difference. This work presents a novel approach to extending the memory of photonic reservoir computing and its timescale of application., Comment: 14 pages, 6 figures

While biological neurons ensure unidirectional signalling, scalable integrated photonic neurons, such as silicon microresonators, respond the same way regardless of excitation direction due to the Lorentz reciprocity principle. Here, we show that a non-linear Taiji microresonator is a proper optical analogous of a biological neuron showing both a spiking response as well as a direction dependence response., Comment: 4 pages and 2 figures

A feed-forward photonic neural network (PNN) is tested for chromatic dispersion compensation in Intensity Modulation/Direct Detection optical links. The PNN is based on a sequence of linear and nonlinear transformations. The linear stage is constituted by an 8-tap time-delayed complex perceptron implemented on a Silicon-On-insulator platform and acting as a tunable optical filter. The nonlinear stage is provided by the square modulus of the electrical field applied at the end-of-line photodetector. The training maximizes the separation between the optical levels (i.e. the eye diagram aperture), with consequent reduction of the Bit Error Rate. Effective equalization is experimentally demonstrated for 20 Gbps 4-level Pulse Amplitude Modulated signal up to 125 km. An evolutionary algorithm and a gradient-based approach are tested for the training and then compared in terms of repeatability and convergence time. The optimal weights resulting from the training are interpreted in light of the theoretical transfer function of the optical fiber. Finally, a simulative study proves the scalability of the layout to larger bandwidths, up to 100 Gbps., Comment: 15 pages, 13 figures

We show how to use universal multiport interferometers' schemes in order to create photonic post-selected Controlled-Z and Controlled-Controlled-Z gates, which are equivalent, modulo single-qubit gates, to Controlled-NOT and Toffoli gates, respectively. The new proposed method is based on the following ingredients: identical single photons, Mach-Zehnder interferometer networks, single-photon detectors and post-selection. In particular, by using dual-rail path encoding together with auxiliary paths and single photons, we improve the success probabilities of such gates. This result further proves the complexity and richness of Reck and Clements schemes beyond the usual notions and practices of Boson Sampling., Comment: 23 pages, 6 figures

In 2021, Adam Zsolt Wagner proposed an approach to disprove conjectures in graph theory using Reinforcement Learning (RL). Wagner's idea can be framed as follows: consider a conjecture, such as a certain quantity f(G) < 0 for every graph G; one can then play a single-player graph-building game, where at each turn the player decides whether to add an edge or not. The game ends when all edges have been considered, resulting in a certain graph G_T, and f(G_T) is the final score of the game; RL is then used to maximize this score. This brilliant idea is as simple as innovative, and it lends itself to systematic generalization. Several different single-player graph-building games can be employed, along with various RL algorithms. Moreover, RL maximizes the cumulative reward, allowing for step-by-step rewards instead of a single final score, provided the final cumulative reward represents the quantity of interest f(G_T). In this paper, we discuss these and various other choices that can be significant in Wagner's framework. As a contribution to this systematization, we present four distinct single-player graph-building games. Each game employs both a step-by-step reward system and a single final score. We also propose a principled approach to select the most suitable neural network architecture for any given conjecture, and introduce a new dataset of graphs labeled with their Laplacian spectra. Furthermore, we provide a counterexample for a conjecture regarding the sum of the matching number and the spectral radius, which is simpler than the example provided in Wagner's original paper. The games have been implemented as environments in the Gymnasium framework, and along with the dataset, are available as open-source supplementary materials., Comment: Accepted at the 27th International Conference on Discovery Science http://ds2024.isti.cnr.it/

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and sub-networks. To a first approximation, this memory can be modelled through a ``plastic'' Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multi-level network structures and ``meta-plastic'' effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional meta-plastic mechanism that varies the rate of Hebbian strengthening of its edge connections. The meta-plastic term acts on a second network level in which edges are grouped together, simulating local, longer time-scale effects. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a meta-plastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorisation) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the meta-reinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, meta-reinforcement allows the retrieval of a previously stored path even after the weights have been reset to zero to erase Hebbian memory., Comment: 14 pages, 9 figures, plus supplementary

Among supervised learning models, Support Vector Machine stands out as one of the most robust and efficient models for classifying data clusters. At the core of this method, a kernel function is employed to calculate the distance between different elements of the dataset, allowing for their classification. Since every kernel function can be expressed as a scalar product, we can estimate it using Quantum Mechanics, where probability amplitudes and scalar products are fundamental objects. The swap test, indeed, is a quantum algorithm capable of computing the scalar product of two arbitrary wavefunctions, potentially enabling a quantum speed-up. Here, we present an integrated photonic circuit designed to implement the swap test algorithm. Our approach relies solely on linear optical integrated components and qudits, represented by single photons from an attenuated laser beam propagating through a set of waveguides. By utilizing 2$^3$ spatial degrees of freedom for the qudits, we can configure all the necessary arrangements to set any two-qubits state and perform the swap test. This simplifies the requirements on the circuitry elements and eliminates the need for non-linearity, heralding, or post-selection to achieve multi-qubits gates. Our photonic swap test circuit successfully encodes two qubits and estimates their scalar product with a measured root mean square error smaller than 0.05. This result paves the way for the development of integrated photonic architectures capable of performing Quantum Machine Learning tasks with robust devices operating at room temperature.

Linear optical quantum computing (LOQC) offers a quantum computation paradigm based on well-established and robust technology and flexible environmental conditions following DiVincenzo's criteria. Within this framework, integrated photonics can be utilized to achieve gate-based quantum computing, defining qubits by path-encoding, quantum gates through the use of Mach-Zehnder interferometers (MZIs) as fundamental building blocks, and measurements through single-photon detectors. In particular, universal two-qubit gates can be achieved by suitable structures of MZIs together with post-selection or heralding. The most resource-efficient choice is given by the post-selected CZ gate. However, this implementation is characterized by a design which has a non-regular structure and cannot be cascaded. This limits the implementation of large-scale LOQC. Starting from these issues, we suggest an approach to move toward a universal and scalable LOQC on the integrated photonic platform. First of all, choosing the post-selected CZ as universal two-qubit gate, we extend the path-encoded dual-rail qubit to a triplet of waveguides, composed of an auxiliary waveguide and the pair of waveguides corresponding to the qubit basis states. Additionally, we introduce a swap photonic network that maps the regularly-labeled structure of the new path-encoded qubits to the structure needed for the post-selected CZ. We also discuss the optical swap gate that allows the connection of non-nearest neighbor path-encoded qubits. In this way, we can deterministically exchange the locations of the qubits and execute controlled quantum gates between any path-encoded qubits. Next, by truncating the auxiliary waveguides after any post-selected CZ, we find that it is possible to cascade this optical gate when it acts on different pairs that share only one qubit.

Silicon oxynitride (SiON) is a low-loss and versatile material for linear and nonlinear photonics applications. Controlling the oxygen-to-nitrogen (O/N) ratio in SiON provides an effective way to engineer its optical and mechanical properties, making it a great platform for the investigation of on-chip optomechanical interactions, especially the stimulated Brillouin scattering (SBS). Here we report the Brillouin nonlinearity characterization of a SiON platform with a specific O/N ratio (characterized by a refractive index of $n=1.65$). First, we introduce this particular SiON platform with fabrication details. Subsequently, we discuss various techniques for the on-chip Brillouin nonlinearity characterizations. In particular, we focus on the intensity-modulated pump-probe lock-in amplifier technique, which enables ultra-sensitive characterization. Finally, we analyze the Brillouin nonlinearities of this SiON platform and compare them with other SiON platforms. This work underscores the potential of SiON for on-chip Brillouin-based applications. Moreover, it paves the way for Brillouin nonlinearity characterization across various material platforms.

Integrated photonics has emerged as one of the most promising platforms for quantum applications. The performances of quantum photonic integrated circuits (QPIC) necessitate a demanding optimization to achieve enhanced properties and tailored characteristics with more stringent requirements with respect to their classical counterparts. In this study, we report on the simulation, fabrication, and characterization of a series of fundamental components for photons manipulation in QPIC based on silicon nitride. These include crossing waveguides, multimode-interferometer-based integrated beam splitters (MMIs), asymmetric integrated Mach-Zehnder interferometers (MZIs) based on MMIs, and micro-ring resonators. Our investigation revolves primarily around the Visible to Near-Infrared spectral region, as these devices are meticulously designed and tailored for optimal operation within this wavelength range. By advancing the development of these elementary building blocks, we aim to pave the way for significant improvements in QPIC in a spectral region only little explored so far., Comment: 13 pages, 10 figures

In this study, we address the challenge of analyzing electrophysiological measurements in neuronal networks. Our computational model, based on the Reservoir Computing Network (RCN) architecture, deciphers spatio-temporal data obtained from electrophysiological measurements of neuronal cultures. By reconstructing the network structure on a macroscopic scale, we reveal the connectivity between neuronal units. Notably, our model outperforms common methods like Cross-Correlation and Transfer-Entropy in predicting the network's connectivity map. Furthermore, we experimentally validate its ability to forecast network responses to specific inputs, including localized optogenetic stimuli., Comment: Submitted version

In this paper we present a computational model which decodes the spatio-temporal data from electro-physiological measurements of neuronal networks and reconstructs the network structure on a macroscopic domain, representing the connectivity between neuronal units. The model is based on reservoir computing network (RCN) approach, where experimental data is used as training and validation data. Consequently, the model can be used to study the functionality of different neuronal cultures and simulate the network response to external stimuli.

The recent progress of artificial intelligence (AI) has boosted the computational possibilities in fields where standard computers are not able to perform. The AI paradigm is to emulate human intelligence and therefore breaks the familiar architecture on which digital computers are based. In particular, neuromorphic computing, artificial neural networks (ANN) and deep learning models mimic how the brain computes. Large networks of interconnected neurons whose synapsis are individually strengthened or weakened during the learning phase find many applications. With this respect, photonics is a suitable platform to implement ANN hardware thanks to its speed, low power dissipation and multi-wavelength opportunities. One photonic device candidate to perform as an optical neuron is the optical microring resonator. Indeed microring resonators show both a nonlinear response and a capability of optical energy storage, which can be interpreted as a fading memory. Moreover, by using silicon photonics, the photonic integrated circuits can be fabricated in volume and with integrated electronics on board. For these reasons, here, we describe the physics of silicon microring resonators and of arrays of microring resonators for application in neuromorphic computing. We describe different types of ANNs from feed-forward networks to photonics extreme learning machines and reservoir computing. In addition, we discuss also hybrid systems where silicon microresonators are coupled to other active materials. this review aims to introduce the basics and to discuss the most recent developments in the field., Comment: 35 pages, 23 figures

In the same silicon photonic integrated circuit, we compare two types of integrated degenerate photon-pair sources (microring resonators or waveguides) by means of Hong-Ou-Mandel (HOM) interference experiments. Two nominally identical microring resonators are coupled to two nominally identical waveguides which form the arms of a Mach-Zehnder interferometer. This is pumped by two lasers at two different wavelengths to generate, by spontaneous four-wave mixing, degenerate photon pairs. In particular, the microring resonators can be thermally tuned in or out of resonance with the pump wavelengths, thus choosing either the microring resonators or the waveguides as photon-pair sources, respectively. In this way, an on-chip HOM visibility of 94% with microring resonators and 99% with straight waveguides is measured upon filtering. We compare our experimental results with theoretical simulations of the joint spectral intensity and the purity of the degenerate photon pairs. We verify that the visibility is connected to the sources' indistinguishability, which can be quantified by the overlap between the joint spectral amplitudes (JSA) of the photon pairs generated by the two sources. We estimate a JSAs overlap of 98% with waveguides and 89% with microring resonators.

Machine learning technologies have found fertile ground in optics due to its promising features based on speed and parallelism. Feed-forward neural networks are one of the most widely used machine learning algorithms due to their simplicity and universal approximation capability. However, the typical training procedure, where all weights are optimized, can be time and energy consuming. An alternative approach is the Extreme Learning Machine, a feed-forward neural network in which only the output weights are trained, while the internal connections are random. Here we present an experimental implementation of a photonic extreme learning machine (PELM) in an integrated silicon chip. The PELM is based on the processing of the image of the scattered light by an array of 18 gratings coupled to microresonators. Light propagation in the microresonator array is a linear process while light detection by the video camera is a nonlinear process. Training is done offline by analyzing the recorded scattered light image with a linear classifier. We provide a proof-of-concept demonstration of the PELM by solving both binary and analog tasks, and show how the performance depends on the number of microresonators used in the readout procedure., Comment: 12 pages and 6 figures

Single-photon entanglement is a peculiar type of entanglement in which two or more degrees of freedom of a single photon are correlated quantum-mechanically. Here, we demonstrate a photonic integrated chip (PIC) able to generate and manipulate single-photon path-entangled states, using a commercial red LED as light source. A Bell test, in the Clauser, Horne, Shimony and Holt (CHSH) form, is performed to confirm the presence of entanglement, resulting in a maximum value of the CHSH correlation parameter equal to $2.605 \pm 0.004$. This allows us to use it as an integrated semi-device independent quantum random number generator able to produce certified random numbers. The certification scheme is based on a Bell's inequality violation and on a partial characterization of the experimental setup, without the need of introducing any further assumptions either on the input state or on the particular form of the measurement observables. In the end a min-entropy of $33\%$ is demonstrated., Comment: 22 pages, 8 figures

Nowadays, Information Photonics is extensively studied and sees applications in many fields. The interest in this breakthrough technology is mainly stimulated by the possibility of achieving real-time data processing for high-bandwidth applications, still implemented through small-footprint devices that would allow for breaking the limit imposed by Moore's law. One potential breakthrough implementation of information photonics is via integrated photonic circuits. Within this approach, the most suitable computational scheme is achieved by integrated photonic neural networks. In this chapter, we provide a review of one possible way to implement a neural network by using silicon photonics. Specifically, we review the work we performed at the Nanoscience Laboratory of the University of Trento. We present methodologies, results, and future challenges about a delayed complex perceptron for fast data processing, a microring resonator exploiting nonlinear dynamics for a reservoir computing approach, and a microring resonator with the addition of a feedback delay loop for time series processing.

Exceptional points, where eigenvalues and eigenvectors coalesce, impact the behavior of different photonics components that show, e.g., enhanced sensing, coherent perfect absorption, unidirectional lasing, and chirality. However, only a few passive geometries have been developed that work on these points. Here, we introduce a novel non-Hermitian structure based on a microresonator shaped as the infinity symbol twice coupled to a bus waveguide: the infinity-loop microresonator. Unlike other structures working on an exceptional surface, the infinity-loop microresonator can achieve either high- or low-contrast unidirectional reflection with a negligible or identical reflection for counterpropagating light. It allows an easy walking through the Riemann sheet by simply controlling the phase of the light propagating in the bus waveguide, which makes it a tunable component to build more complex topological structures. Furthermore, the infinity-loop microresonator allows sensors that show the features of both an exceptional point device and a diabolic point device simultaneously., Comment: 14 pages, 12 figures

A small 4-channels time-delayed complex perceptron is used as a silicon photonics neural network (NN) device to compensate for chromatic dispersion in optical fiber links. The NN device is experimentally tested with non-return-to-zero optical signals at 10 Gbps after propagation through up to 125 km optical fiber link. During the learning phase, a separation-loss function is optimized in order to maximally separate the transmitted levels of 0s from the 1s, which implies an optimization of the bit-error-rate. Testing of the NN device shows that the excess losses introduced by the NN device are compensated by the gain in transmitted signal equalization for a link longer than 100 km. The measured data are reproduced by a model which accounts for the optical link and the neural network device. This allows simulating the network performances for higher data rates, where the device shows improvement with respect to the benchmark both in terms of performance as well as ease of use., Comment: 14 pages, 6 figures