Photon liquefaction in time
We provide a mechanism to imprint local temporal correlations in photon streams which have the same character as spatial correlations in liquids. Usual single-photon emitters correspond, in this picture, to a (temporal) gas while uncorrelated light is the ideal gas. We argue that good single-photon sources are those that exhibit such temporal liquid features, i.e., with a plateau for their short-time correlations (as opposed to a linear dependence) and oscillations at later times, which is a direct manifestation of photon time-ordering. We obtain general, closed-form analytical expressions for the second-order coherence function of a broad family of “liquid light” which can be arbitrarily correlated, though never completely crystallized.
Spatial correlations of vortex quantum states
We study spatial correlations of vortices in different quantum states or with Bose or Fermi statistics. This is relevant for both optical vortices and condensed-matter ones such as microcavity polaritons, or any platform that can prepare and image fields in space at the few-particle level. While we focus on this particular case for illustration of the formalism, we already reveal unexpected features of spatial condensation whereby bosons exhibit a bimodal distribution of their distances which places them farther apart than fermions in over 40% of the cases, or on the opposite conceal spatial correlations to behave like coherent states. Such experiments upgrade in the laboratory successful techniques in uncontrolled extreme environments (stars and nuclei).
Benchmarking the optimization optical machines with the planted solutions
We introduce universal, easy-to-reproduce generative models for the QUBO instances to differentiate the performance of the hardware/solvers effectively. Our benchmark process extends the well-known Hebb’s rule of associative memory with the asymmetric pattern weights. We provide a comprehensive overview of calculations conducted across various scales and using different classes of dynamical equations. Our aim is to analyze their results, including factors such as the probability of encountering the ground state, planted state, spurious state, or states falling outside the predetermined energy range. Moreover, the generated problems show additional properties, such as the easy-hard-easy complexity transition and complicated cluster structures of planted solutions. Our method establishes a prospective platform to potentially address other questions related to the fundamental principles behind device physics and algorithms for novel computing machines.
Classical vs Quantum annealing and manifold reduction in soft-spin minimizers of Ising Hamiltonians
We investigate the minimization of the Ising Hamiltonians, comparing the dynamics of semi- classical soft-spin models with quantum annealing. We systematically analyze how the energy landscape for the circulant couplings of a M¨obius graph evolves with increased annealing parameters. Our findings indicate that these semi-classical models face challenges due to a widening dimensionality landscape. To counteract this issue, we introduce the ‘manifold reduction’ method, which restricts the soft-spin amplitudes to a defined phase space region. Concurrently, quantum annealing demonstrates a natural capability to navigate the Ising Hamiltonian’s energy landscape due to its operation within the comprehensive Hilbert space. Our study indicates that physics-inspired or physics-enhanced optimizers will likely benefit from a blend of classical and quantum annealing techniques.
Macroscopic noise amplification by asymmetric dyads in non-Hermitian optical systems for generative diffusion models
A new generation of sensors, hardware random number generators, and quantum and classical signal detectors are exploiting strong responses to external perturbations or system noise. Here, we study noise amplification by asymmetric dyads in freely expanding non-Hermitian optical systems. We show that modifications of the pumping strengths can counteract bias from natural imperfections of the system’s hardware, while couplings between dyads lead to systems with non-uniform statistical distributions. Our results suggest that asymmetric non-Hermitian dyads are promising candidates for efficient sensors and ultra-fast random number generators. We propose that the integrated light emission from such asymmetric dyads can be efficiently used for an analog all-optical degenerative diffusion models of machine learning to overcome the digital limitations of such models in processing speed and energy consumption.
Published in Physical Review Letters
Beyond Digital: harnessing analog hardware for machine learning
A remarkable surge in utilizing large deep-learning models yields state-of-the-art results in a variety of tasks. Recent model sizes often exceed billions of parameters, underscoring the importance of fast and energy-efficient processing. The significant costs associated with training and inference primarily stem from the constrained memory bandwidth of current hardware and the computationally intensive nature of these models. Historically, the design of machine learning models has predominantly been guided by the operational parameters of classical digital devices. In contrast, analog computations have the potential to offer vastly improved power efficiency for both inference and training tasks. This work details several machine-learning methodologies that could leverage existing analog hardware infrastructures. To foster the development of analog hardware-aware machine learning techniques, we explore both optical and electronic hardware configurations suitable for executing the fundamental mathematical operations inherent to these models. Integrating analog hardware with innovative machine learning approaches may pave the way for cost-effective AI systems at scale.
Vector Ising Spin Annealer for Minimizing Ising Hamiltonians
We introduce the Vector Ising Spin Annealer (VISA), a framework in gain-based computing that harnesses light-matter interactions to solve complex optimization problems encoded in spin Hamiltonians. Traditional driven-dissipative systems often select excited states due to limitations in spin movement. VISA transcends these constraints by enabling spins to operate in a three-dimensional space, offering a robust solution to minimize Ising Hamiltonians effectively. Our comparative analysis reveals VISA’ s superior performance over conventional single-dimension spin optimizers, demonstrating its ability to bridge substantial energy barriers in complex landscapes. Through detailed studies on cyclic and random graphs, we show VISA’s proficiency in dynamically evolving the energy landscape with time-dependent gain and penalty annealing, illustrating its potential to redefine optimization in physical systems.
Coupling Light with Matter for Identifying Dominant Subnetworks
We present a novel light-matter platform that uses complex-valued oscillator networks, a form of physical neural networks, to identify dominant subnetworks and uncover indirect correlations within larger networks. This approach offers significant advantages, including low energy consumption, high processing speed, and the immediate identification of co- and counter-regulated nodes without post-processing. The effectiveness of this approach is demonstrated through its application to biological networks, and we also propose its applicability to a wide range of other network types.
Optimal quantum key distribution networks: capacitance versus security
The rate and security of quantum communications between users placed at arbitrary points of a quantum communication network depend on the structure of the network, on its extension and on the nature of the communication channels. In this work we propose a strategy for the optimization of trusted-relays based networks that intertwines classical network approaches and quantum information theory. Specifically, by suitably defining a quantum communication efficiency functional, we identify the optimal quantum communication connections through the network by balancing security and the quantum communication rate. The optimized network is then constructed as the network of the maximal quantum communication efficiency connections and its performance is evaluated by studying the scaling of average properties as functions of the number of nodes and of the network spatial extension.
Published in npj Quantum Information
Efficient Computation Using Spatial-Photonic Ising Machines: Utilizing Low-Rank and Circulant Matrix Constraints
We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically affected by the rank and precision of the coupling matrices. By developing and assessing advanced decomposition techniques, we expand the range of problems SPIMs can solve, overcoming the limitations of traditional Mattis-type matrices. Our approach accommodates a diverse array of coupling matrices, including those with inherently low ranks, applicable to complex NP-complete problems. We explore the practical benefits of low-rank approximation in optimization tasks, particularly in financial optimization, to demonstrate the real-world applications of SPIMs. Finally, we evaluate the computational limitations imposed by SPIM hardware precision and suggest strategies to optimize the performance of these systems within these constraints.
Localization in Quantum Field Theory
We review the issue of localization in quantum field theory and detail the nonrelativistic limit. Three distinct localization schemes are examined: the Newton–Wigner, the algebraic quantum field theory, and the modal scheme. Among these, the algebraic quantum field theory provides a fundamental concept of localization, rooted in its axiomatic formulation. In contrast, the Newton–Wigner scheme draws inspiration from the Born interpretation, applying mainly to the nonrelativistic regime. The modal scheme, relying on the representation of single particles as positive frequency modes of the Klein–Gordon equation, is found to be incompatible with the algebraic quantum field theory localization.
This review delves into the distinctive features of each scheme, offering a comparative analysis. A specific focus is placed on the property of independence between state preparations and observable measurements in spacelike separated regions. Notably, the notion of localization in algebraic quantum field theory violates this independence due to the Reeh–Schlieder theorem. Drawing parallels with the quantum teleportation protocol, it is argued that causality remains unviolated. Additionally, we consider the nonrelativistic limit of quantum field theory, revealing the emergence of the Born scheme as the fundamental concept of localization. Consequently, the nonlocality associated with the Reeh–Schlieder theorem is shown to be suppressed under nonrelativistic conditions.
Published in Reviews in Physics
Qubit analog with polariton superfluid in an annular trap
We report on the experimental realization and characterization of a qubit analog with semiconductor exciton-polaritons. In our system, a polaritonic condensate is confined by a spatially patterned pump laser in an annular trap that supports energy-degenerate vortex states of the polariton superfluid. Using temporal interference measurements, we observe coherent oscillations between a pair of counter-circulating vortex states coupled by elastic scattering of polaritons off the laser-imprinted potential. The qubit basis states correspond to the symmetric and antisymmetric superpositions of the two vortex states. By engineering the potential, we tune the coupling and coherent oscillations between the two circulating current states, control the energies of the qubit basis states, and initialize the qubit in the desired state. The dynamics of the system is accurately reproduced by our theoretical two-state model, and we discuss potential avenues to implement quantum gates and algorithms with polaritonic qubits analogous to quantum computation with standard qubits.
Ising Hamiltonian minimization: Gain-based computing with manifold reduction of soft spins vs quantum annealing
We investigate the minimization of Ising Hamiltonians, comparing the performance of gain-based computing paradigms based on the dynamics of semiclassical soft-spin models with quantum annealing. We systematically analyze how the energy landscape for the circulant couplings of a Möbius graph evolves with increased annealing parameters. Our findings indicate that these semiclassical models face challenges due to a widening dimensionality landscape. To counteract this issue, we introduce the manifold reduction method, which restricts the soft-spin amplitudes to a defined phase space region. Concurrently, quantum annealing demonstrates a natural capability to navigate the Ising Hamiltonian’s energy landscape due to its operation within the comprehensive Hilbert space. Our study indicates that physics-inspired or physics-enhanced optimizers will likely benefit from combining classical and quantum annealing techniques.
Published in Physical Review Research
Unlocking multiphoton emission from a single-photon source through mean-field engineering
Single-photon emission from a two-level system offers promising perspectives for the development of quantum technologies, where multiphotons are generally regarded as accidental, undesired and should be suppressed. In quantum mechanics, however, multiphoton emission can turn out to be even more fundamental and interesting than the single-photon emission, since in a coherently driven system, the multiphoton suppression arises from quantum interferences between virtual multiphoton fluctuations and the mean field in a Poisson superposition of all number states. Here, we demonstrate how one can control the multiphoton dynamics of a two-level system by disrupting these quantum interferences through a precise and independent homodyne control of the mean field. We show that, counterintuitively, quantum fluctuations always play a major qualitative role, even and in fact especially, when their quantitative contribution is vanishing as compared to that of the mean field. Our findings provide new insights into the paradoxical character of quantum mechanics and open pathways for mean-field engineering as a tool for precision multiphoton control.
Complex vector gain-based annealer for minimizing XY Hamiltonians
This paper presents the Complex Vector Gain-Based Annealer (CoVeGA), an analog computing platform designed to overcome energy barriers in XY Hamiltonians through a higher-dimensional representation. Traditional gain-based solvers utilizing optical or photonic hardware typically represent each XY spin with a single complex field. These solvers often struggle with large energy barriers in complex landscapes, leading to relaxation into excited states. CoVeGA addresses these limitations by employing two complex fields to represent each XY spin and dynamically evolving the energy landscape through time-dependent annealing. Operating in a higher-dimensional space, CoVeGA bridges energy barriers in this expanded space during the continuous phase evolution, thus avoiding entrapment in local minima. We introduce several graph structures that pose challenges for XY minimization and use them to benchmark CoVeGA against single-dimension XY solvers, highlighting the benefits of higher-dimensional operation.
Observation of 2D dam break flow and a gaseous phase of solitons in a photon fluid
We report the observation of a two-dimensional dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to two-dimensional (2D) nonlinear dynamics. We observe
wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D solitons gas in integrable systems. We measure the statistical features of this gaseous-like phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.
Correlations in Circular Quantum Cascades
We introduce a one-way, one-quantum cascade, whereby a single excitation proceeds one-directionwise in a ladder of energy levels. This makes a variation from more famous two-way cascades where the excitation can go up and down following its excitation or relaxation in the ladder. We provide closed-form solutions for two-photon correlation functions between any transitions in such circular cascades. We discuss how the rich correlations that result from what appears to be an extremely simple implementation, are essentially those which have been entertained from
complex architectures relying on strongly-correlated, many-body physics or cavity QED effects.
Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines
Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising Machines have proven to be advantageous for simulating fully connected large-scale spin systems. However, fine control of a general interaction matrix J has so far only been accomplished through eigenvalue decomposition methods that either limit the scalability or increase the execution time of the optimization process. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, enabling the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system, and paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models, on SPIM devices.
Training of Physical Neural Networks
Physical neural networks (PNNs) are a class of neural-like networks that leverage the properties of physical systems to perform computation. While PNNs are so far a niche research area with small-scale laboratory demonstrations, they are arguably one of the most underappreciated important opportunities in modern artificial intelligence (AI). Could we train AI models 1000x larger than current ones? Could we do this and also have them perform inference locally and privately on edge devices, such as smartphones or sensors? Research over the past few years has shown that the answer to all these questions is likely “textityes, with enough research”: PNNs could one day radically change what is possible and practical for AI systems. To do this will however require rethinking both how AI models work, and how they are trained – primarily by considering the problems through the constraints of the underlying hardware physics. To train PNNs at large scale, many methods including backpropagation-based and backpropagation-free approaches are now being explored. These methods have various trade-offs, and so far no method has been shown to scale to the same scale and performance as the backpropagation algorithm widely used in deep learning today. However, this is rapidly changing, and a diverse ecosystem of training techniques provides clues for how PNNs may one day be utilized to create both more efficient realizations of current-scale AI models, and to enable unprecedented-scale models.
A Fully Analog Pipeline for Portfolio Optimization
Portfolio optimization is a ubiquitous problem in financial mathematics that relies on accurate estimates of covariance matrices for asset returns. However, estimates of pairwise covariance could be better and calculating time-sensitive optimal portfolios is energy-intensive for digital computers. We present an energy-efficient, fast, and fully analog pipeline for solving portfolio optimization problems that overcomes these limitations. The analog paradigm leverages the fundamental principles of physics to recover accurate optimal portfolios in a two-step process. Firstly, we utilize equilibrium propagation, an analog alternative to backpropagation, to train linear autoencoder neural networks to calculate low-rank covariance matrices. Then, analog continuous Hopfield networks output the minimum variance portfolio for a given desired expected return. The entire efficient frontier may then be recovered, and an optimal portfolio selected based on risk appetite.
Localization in Quantum Field Theory for inertial and accelerated observers
We study the problem of localization in Quantum Field Theory (QFT) from the point of view of inertial and accelerated experimenters. We consider the Newton-Wigner, the Algebraic Quantum Field Theory (AQFT) and the modal localization schemes, which are, respectively, based on the orthogonality condition for states localized in disjoint regions of space, on the algebraic approach to QFT and on the representation of single particles as positive frequency solution of the field equation. We show that only the AQFT scheme obeys causality and physical invariance under diffeomorphisms. Then, we consider the nonrelativistic limit of quantum fields in the Rindler frame. We demonstrate the convergence between the AQFT and the modal scheme and we show the emergence of the Born notion of localization of states and observables. Also, we study the scenario in which an experimenter prepares states over a background vacuum by means of nonrelativistic local operators and another experimenter carries out nonrelativistic local measurements in a different region. We find that the independence between preparation of states and measurements is not guaranteed when both experimenters are accelerated and the background state is different from Rindler vacuum, or when one of the two experimenters is inertial.
Fully Programmable Spatial Photonic Ising Machine by Focal Plane Division
Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to accelerate the computation, showcasing parallelism, scalability, and low power consumption. However, current SPIMs can implement only a restricted class of problems. This partial programmability is a critical limitation that hampers their benchmark. Achieving full programmability of the device while preserving its scalability is an open challenge.
Here, we report a fully programmable SPIM achieved through a novel operation method based on the division of the focal plane. In our scheme, a general Ising problem is decomposed into a set of Mattis Hamiltonians, whose energies are simultaneously computed optically by measuring the intensity on different regions of the camera sensor. Exploiting this concept, we experimentally demonstrate the computation with high success probability of ground-state solutions of up to 32-spin Ising models on unweighted maximum cut graphs with and without ferromagnetic bias. Simulations of the hardware prove a favorable scaling of the accuracy with the number of spin. Our fully programmable SPIM enables the implementation of many quadratic unconstrained binary optimization problems, further establishing SPIMs as a leading paradigm in non von Neumann hardware.
Published in Physical Review Letters
Roadmap on Neuromorphic Photonics
Neuromorphic photonics are processors inspired by the human brain and enabled by light (photons) instead of traditional electronics. Neuromorphic photonics and its associated concepts are experiencing a significant resurgence, building on foundational research from the 1980s and 1990s. This renewed momentum is driven by breakthroughs in photonic integration, nonlinear optics, and advanced materials, alongside the growing necessity of neuro-inspired computing in numerous applications of economic and societal relevance. The increasing demand for energy-efficient artificial intelligence (AI) solutions underscores the need for innovation and a cohesive vision to address key challenges, including scalability, energy efficiency, precision, and standardized performance benchmarks. Together, these efforts present an opportunity to establish a unique photonic advantage with practical, real-world applications. 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. The roadmap introduces various approaches to embedding the high-complexity transformations central to neuromorphic computing, focusing on frequency, delay, and spectral embeddings. This is followed by a discussion of architectures of photonic neural networks (PNNs) and an in-depth analysis of methods for implementing these architectures in photonic hardware. Dedicated sections delve into integrated photonic hardware, the realization of photonic weights and memories, and the optimization of training processes for photonic neuromorphic architectures. The roadmap concludes by exploring numerous potential applications, highlighting the challenges and advances necessary to transition neuromorphic photonic computing from a primarily academic pursuit to a technology with economic and societal impact. By synthesizing contributions from over 40 research teams, this roadmap aims to provide the photonics community with a comprehensive framework for unlocking the transformative potential of PNNs in advancing AI and beyond.
