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A mathematical description of the reduced dynamics of an open quantum system can often be given in terms of a completely positive and trace preserving (CPTP) map, also known as quantum channel. In a seminal work by Wolf et al. [Phys. Rev. Lett. 101, 150402 (2008)], it was shown that deciding whether a given quantum channel was generated from an underlying effective Markovian dynamics, with time-independent Lindbladian generator, is generally an NP-hard problem. In this work we show that in cases where one has access to the full reduced dynamics at all previous times (the dynamical map) one can significantly facilitate the search for an effective generator by making use of Floquet theory. By performing a spectral unwinding such that the effective micromotion is minimized, the effective Floquet generator is often an excellent candidate for an effective Lindblad generator, hence significantly reducing the complexity of the search for an effective Lindblad generator in many (though not all) cases. Our results are relevant for engineering Floquet Lindbladians in complex many-body systems.

Diffusion models generate new samples by progressively decreasing the noise from the initially provided random distribution. This inference procedure generally utilizes a trained neural network numerous times to obtain the final output, creating significant latency and energy consumption on digital electronic hardware such as GPUs. In this study, we demonstrate that the propagation of a light beam through a semi-transparent medium can be programmed to implement a denoising diffusion model on image samples. This framework projects noisy image patterns through passive diffractive optical layers, which collectively only transmit the predicted noise term in the image. The optical transparent layers, which are trained with an online training approach, backpropagating the error to the analytical model of the system, are passive and kept the same across different steps of denoising. Hence this method enables high-speed image generation with minimal power consumption, benefiting from the bandwidth and energy efficiency of optical information processing., Comment: 14 pages, 6 figures

Electronic computers have evolved drastically over the past years with an ever-growing demand for improved performance. However, the transfer of information from memory and high energy consumption have emerged as issues that require solutions. Optical techniques are considered promising solutions to these problems with higher speed than their electronic counterparts and with reduced energy consumption. Here, we use the optical reservoir computing framework we have previously described (Scalable Optical Learning Operator or SOLO) to program the spatial-spectral output of the light after nonlinear propagation in a multimode fiber. The novelty in the current paper is that the system is programmed through an output sampling scheme, similar to that used in hyperspectral imaging in astronomy. Linear and nonlinear computations are performed by light in the multimode fiber and the high dimensional spatial-spectral information at the fiber output is optically programmed before it reaches the camera. We then used a digital computer to classify the programmed output of the multi-mode fiber using a simple, single layer network. When combining front-end programming and the proposed spatial-spectral programming, we were able to achieve 89.9% classification accuracy on the dataset consisting of chest X-ray images from COVID-19 patients. At the same time, we obtained a decrease of 99% in the number of tunable parameters compared to an equivalently performing digital neural network. These results show that the performance of programmed SOLO is comparable with cutting-edge electronic computing platforms, albeit with a much-reduced number of electronic operations.

Artificial Intelligence (AI) demands large data flows within datacenters, heavily relying on multicasting data transfers. As AI models scale, the requirement for high-bandwidth and low-latency networking compounds. The common use of electrical packet switching faces limitations due to optical-electrical-optical conversion bottlenecks. Optical switches, while bandwidth-agnostic and low-latency, suffer from having only unicast or non-scalable multicasting capability. This paper introduces an optical switching technique addressing this challenge. Our approach enables arbitrarily programmable simultaneous unicast and multicast connectivity, eliminating the need for optical splitters that hinder scalability due to optical power loss. We use phase modulation in multiple layers, tailored to implement any multicast connectivity map. Phase modulation also enables wavelength selectivity on top of spatial selectivity, resulting in an optical switch that implements space-wavelength routing. We conducted simulations and experiments to validate our approach. Our results affirm the concept's feasibility, effectiveness, and scalability, as a multicasting switch by experimentally demonstrating 16 spatial ports using 2 wavelength channels. Numerically, 64 spatial ports with 4 wavelength channels each were simulated, with approximately constant efficiency (< 3 dB) as ports and wavelength channels scale., Comment: 17 pages, 4 figures, article

Phase imaging is widely used in biomedical imaging, sensing, and material characterization, among other fields. However, direct imaging of phase objects with subwavelength resolution remains a challenge. Here, we demonstrate subwavelength imaging of phase and amplitude objects based on all-optical diffractive encoding and decoding. To resolve subwavelength features of an object, the diffractive imager uses a thin, high-index solid-immersion layer to transmit high-frequency information of the object to a spatially-optimized diffractive encoder, which converts/encodes high-frequency information of the input into low-frequency spatial modes for transmission through air. The subsequent diffractive decoder layers (in air) are jointly designed with the encoder using deep-learning-based optimization, and communicate with the encoder layer to create magnified images of input objects at its output, revealing subwavelength features that would otherwise be washed away due to diffraction limit. We demonstrate that this all-optical collaboration between a diffractive solid-immersion encoder and the following decoder layers in air can resolve subwavelength phase and amplitude features of input objects in a highly compact design. To experimentally demonstrate its proof-of-concept, we used terahertz radiation and developed a fabrication method for creating monolithic multi-layer diffractive processors. Through these monolithically fabricated diffractive encoder-decoder pairs, we demonstrated phase-to-intensity transformations and all-optically reconstructed subwavelength phase features of input objects by directly transforming them into magnified intensity features at the output. This solid-immersion-based diffractive imager, with its compact and cost-effective design, can find wide-ranging applications in bioimaging, endoscopy, sensing and materials characterization., Comment: 32 Pages, 9 Figures

Advances in optical and electrophysiological recording technologies have made it possible to record the dynamics of thousands of neurons, opening up new possibilities for interpreting and controlling large neural populations in behaving animals. A promising way to extract computational principles from these large datasets is to train data-constrained recurrent neural networks (dRNNs). Performing this training in real-time could open doors for research techniques and medical applications to model and control interventions at single-cell resolution and drive desired forms of animal behavior. However, existing training algorithms for dRNNs are inefficient and have limited scalability, making it a challenge to analyze large neural recordings even in offline scenarios. To address these issues, we introduce a training method termed Convex Optimization of Recurrent Neural Networks (CORNN). In studies of simulated recordings, CORNN attained training speeds ~100-fold faster than traditional optimization approaches while maintaining or enhancing modeling accuracy. We further validated CORNN on simulations with thousands of cells that performed simple computations such as those of a 3-bit flip-flop or the execution of a timed response. Finally, we showed that CORNN can robustly reproduce network dynamics and underlying attractor structures despite mismatches between generator and inference models, severe subsampling of observed neurons, or mismatches in neural time-scales. Overall, by training dRNNs with millions of parameters in subminute processing times on a standard computer, CORNN constitutes a first step towards real-time network reproduction constrained on large-scale neural recordings and a powerful computational tool for advancing the understanding of neural computation., Comment: Accepted at NeurIPS 2023

We demonstrate the fabrication of volume holograms using 2-photon polymerization with dynamic control of light exposure. We refer to our method as (3+1)D printing. Volume holograms that are recorded by interfering reference and signal beams have a diffraction efficiency relation that is inversely proportional with the square of the number of superimposed holograms. By using (3+1)D printing for fabrication, the refractive index of each voxel is created independently and thus by, digitally filtering the undesired interference terms, the diffraction efficiency is now inversely proportional to the number of multiplexed gratings. We experimentally demonstrated this linear dependence by recording M=50 volume gratings. To the best of our knowledge, this is the first experimental demonstration of distributed volume holograms that overcome the 1/M^2 limit., Comment: 8 pages, 9 figures

Deep neural networks have achieved remarkable breakthroughs by leveraging multiple layers of data processing to extract hidden representations, albeit at the cost of large electronic computing power. To enhance energy efficiency and speed, the optical implementation of neural networks aims to harness the advantages of optical bandwidth and the energy efficiency of optical interconnections. In the absence of low-power optical nonlinearities, the challenge in the implementation of multilayer optical networks lies in realizing multiple optical layers without resorting to electronic components. In this study, we present a novel framework that uses multiple scattering that is capable of synthesizing programmable linear and nonlinear transformations concurrently at low optical power by leveraging the nonlinear relationship between the scattering potential, represented by data, and the scattered field. Theoretical and experimental investigations show that repeating the data by multiple scattering enables non-linear optical computing at low power continuous wave light. Moreover, we empirically found that scaling of this optical framework follows the power law as in state-of-the-art deep digital networks., Comment: 15 pages and 5 figures

Neural networks (NN) have demonstrated remarkable capabilities in various tasks, but their computation-intensive nature demands faster and more energy-efficient hardware implementations. Optics-based platforms, using technologies such as silicon photonics and spatial light modulators, offer promising avenues for achieving this goal. However, training multiple trainable layers in tandem with these physical systems poses challenges, as they are difficult to fully characterize and describe with differentiable functions, hindering the use of error backpropagation algorithm. The recently introduced Forward-Forward Algorithm (FFA) eliminates the need for perfect characterization of the learning system and shows promise for efficient training with large numbers of programmable parameters. The FFA does not require backpropagating an error signal to update the weights, rather the weights are updated by only sending information in one direction. The local loss function for each set of trainable weights enables low-power analog hardware implementations without resorting to metaheuristic algorithms or reinforcement learning. In this paper, we present an experiment utilizing multimode nonlinear wave propagation in an optical fiber demonstrating the feasibility of the FFA approach using an optical system. The results show that incorporating optical transforms in multilayer NN architectures trained with the FFA, can lead to performance improvements, even with a relatively small number of trainable weights. The proposed method offers a new path to the challenge of training optical NNs and provides insights into leveraging physical transformations for enhancing NN performance.

The recent advancement of large language models presents numerous opportunities for teaching and learning. Despite widespread public debate regarding the use of large language models, empirical research on their opportunities and risks in education remains limited. In this work, we demonstrate the qualities and shortcomings of using ChatGPT 3.5 for physics task development by prospective teachers. In a randomized controlled trial, 26 prospective physics teacher students were divided into two groups: the first group used ChatGPT 3.5 to develop text-based physics tasks for four different concepts in the field of kinematics for 10th grade high school students, while the second group used a classical textbook to create tasks for the same concepts and target group. The results indicate no difference in task correctness, but students using the textbook achieved a higher clarity and more frequently embedded their questions in a meaningful context. Both groups adapted the level of task difficulty easily to the target group but struggled strongly with sufficient task specificity, i.e., relevant information to solve the tasks were missing. Students using ChatGPT for problem posing rated high system usability but experienced difficulties with output quality. These results provide insights into the opportunities and pitfalls of using large language models in education., Comment: 10 pages, 3 figures, 3 tables

The universe is a vast heterogeneous network of interconnected entities that continuously generate and exchange information through various forms of interactions, some of which are yet to be discovered. Internet of Everything (IoE) framework, inspired by the ubiquitous and adaptive connectivity and the seamless interoperability within this universal network, puts forward a new road map beyond the conventional Internet of Things (IoT) towards maximizing the resolution of our interface with the universe to enable unprecedented applications. The first pillar of this road map is to reveal novel and tangible interconnections between seemingly noninteracting branches of IoT, which we call IoXs with X referring to their application domains, e.g., Internet of Energy (IoEn), Internet of Vehicles (IoV). The second pillar is to develop new IoXs that can complement the existing ones to complete the overall IoE picture and match its networking traits to that of the universe for a seamless and all-embracing cyber-physical interface. The objective of this paper is to evaluate the potential of this holistic IoE approach to expand the limited application landscape of the current IoT practice on a scale ranging $\textit{from molecules to the universe}$. To this end, we identify several potential interaction pathways among IoXs and introduce novel and emerging IoXs that are essential to the comprehensiveness of IoE. We also discuss the potential applications that can be enabled by such interconnections within the IoE framework and identify the associated challenges.

In this paper we study the radial epiderivative notion for nonconvex functions, which extends the (classical) directional derivative concept. The paper presents new definition and new properties for this notion and establishes relationships between the radial epiderivative, the Clarke's directional derivative, the Rockafellar's subderivative and the directional derivative. The radial epiderivative notion is used to establish new regularity conditions without convexity conditions. The paper analyzes necessary and sufficient conditions for global optimums in nonconvex optimization via the generalized derivatives studied in this paper. We establish a necessary and sufficient condition for a descent direction for radially epidifferentiable nonconvex functions. The paper presents explicit formulations for computing the weak subgradients in terms of the radial epiderivatives and vice versa, which are very important from point of view of developing solution methods for finding global optimums in nonsmooth and nonconvex optimization. All the properties and theorems presented in this paper, are illustrated and interpreted on examples.

We study the scattering of a single photon propagating along a waveguide in an arbitrary superposition state two frequencies with a single three-level $\Lambda$ atom in a superposition of two non-degenerate ground states where the atom is coupled to a waveguide. We find that the scattering depends on both the relative phase between the photon frequencies and the relative phase between the atomic ground states. Our results show that a three-level $\Lambda$ atom coupled to a waveguide can be used as photon phase filter that could detect the relative phase between the two frequencies of the photon superposition state., Comment: Comments welcome :)

The ever-increasing demand for processing data with larger machine learning models requires more efficient hardware solutions due to limitations such as power dissipation and scalability. Optics is a promising contender for providing lower power computation since light propagation through a non-absorbing medium is a lossless operation. However, to carry out useful and efficient computations with light, generating and controlling nonlinearity optically is a necessity that is still elusive. Multimode fibers (MMF) have been shown that they can provide nonlinear effects with microwatts of average power while maintaining parallelism and low loss. In this work, we propose an optical neural network architecture, which performs nonlinear optical computation by controlling the propagation of ultrashort pulses in MMF by wavefront shaping. With a surrogate model, optimal sets of parameters are found to program this optical computer for different tasks with minimal utilization of an electronic computer. We show a remarkable decrease of 97% in the number of model parameters, which leads to an overall 99% digital operation reduction compared to an equivalently performing digital neural network. We further demonstrate that a fully optical implementation can also be performed with competitive accuracies., Comment: 32 pages, 11 figures

Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised machine learning. The common feature of all algorithms is that they employ an incremental quasi-Newton (IQN) strategy, specifically an incremental BFGS (IBFGS) strategy. One applies an IBFGS strategy to the problem directly, whereas the others apply an IBFGS strategy to a difference-of-convex reformulation, smoothed approximation, or (strongly) convex local approximation. Experiments show that all IBFGS approaches fare well in practice, and all outperform a state-of-the-art bundle method.