Programming multi-level quantum gates in disordered computing reservoirs via machine learning and TensorFlow

Novel machine learning computational tools open new perspectives for quantum information systems. Here we adopt the open-source programming library TensorFlow to design multi-level quantum gates including a computing reservoir represented by a random unitary matrix. In optics, the reservoir is a disordered medium or a multi-modal fiber. We show that trainable operators at the input and the readout enable one to realize multi-level gates. We study various qudit gates, including the scaling properties of the algorithms with the size of the reservoir. Despite an initial low slop learning stage, TensorFlow turns out to be an extremely versatile resource for designing gates with complex media, including different models that use spatial light modulators with quantized modulation levels.Comment: Added a new section and a new figure about implementation of the gates by a single spatial light modulator. 9 pages and 4 figure

Nonlinear optical waves in disordered ferroelectrics

This thesis describes an experimental, numerical and theoretical investigation of nonlinear optical phenomena in disordered photorefractive ferroelectrics in proximity of their phase-transition temperature. The work addresses different physical issues that find in nonlinear optics a common fertile research arena and are closely related to each other in the considered systems. Nonlinear wave dynamics in the spatial domain, where self-interaction of propagating waves generally results into non-spreading localized wavepackets such as spatial solitons, is extended in photorefractive ferroelectrics to non-equilibrium regimes characterized by stochastic instabilities and large material fluctuations. We discover the emergence of rogue waves, localized perturbations of abnormal intensity, whose understanding is challenging in various physical contexts and resides in the general problem of long-tail statistical distributions in complex systems. We identify their origin in spatiotemporal soliton dynamics in a saturable nonlinearity which can support scale-invariant waveforms. Properties and predictability of the observed extreme events are investigated, and, in particular, we demonstrate their active control through the spatial incoherence scale of the optical field. Moreover, we report how their emergence is sustained by turbulent transitions to an incoherent and disordered optical state triggered by modulational instability. The onset of strong turbulence for propagating optical waves has remained unobserved up to now and our results demonstrate a new experimental setting for its study. When the functional form of the nonlinearity is turned into a nonlocal one due to diffusive fields, this setting also exploits photonics to address fundamental physical problems and access to otherwise hidden phenomena. The natural spreading of waves during propagation, representing the wavelength-defined ultimate limit to spatial resolution, can be eliminated and reversed leading to diffraction cancellation and anti-diffraction of light. Since these behaviors on modifying the nature of underlying Schrödinger equation, we are the first to demonstrate how nonlinearity can make the spatial light distribution behave as the wavefunction of a quantum particle with negative mass. All these findings have roots in the nonlinear optical response of critical disordered ferroelectric crystals, which are also extremely interesting from the condensed matter point of view. In fact, competition of different microscopic structural phases and the associated polar-domain dynamics at the nanoscale results into non-ergodic dipolar-glass behaviors giving giant responses such as giant polarization, piezoelectricity and electro-optic effect. Disordered ferroelectrics crystals are investigated electro-optically across their ferroelectric phase-transition, where we report the observation of an anomalous electro-optic effect compatible with ultracold dipolar reorientation. In compounds presenting spatial inhomogeneity in their chemical composition, we discover a new ferroelectric phase of matter in which polar domains spontaneously coordinate into a mesoscopic coherent polarization super-crystals. This phase mimics standard solid-state structures but on scales that are thousands of times larger and represent the first spontaneous three-dimensional photonic crystal

Adiabatic evolution on a spatial-photonic Ising machine

Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware.Novel optical platforms, knownas coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-known technique based on adiabatic evolution for finding optimal solutions in classical and quantum systems made by atoms, electrons, or photons. Although various Ising machines employ annealing in some form, adiabatic computing on optical settings has been only partially investigated.Here, we realize the adiabatic evolution of frustrated Ising models with 100 spins programmed by spatial light modulation. We use holographic and optical control to change the spin couplings adiabatically, and exploit experimental noise to explore the energy landscape. Annealing enhances the convergence to the Ising ground state and allows to find the problem solution with probability close to unity.Our results demonstrate a photonic scheme for combinatorial optimization in analogy with adiabatic quantum algorithms and classical annealing methods but enforced by optical vector-matrix multiplications and scalable photonic technology

Synchrotron resonant radiation from nonlinear self-accelerating pulses

Solitons and nonlinear waves emit resonant radiation in the presence of perturbations. This effect is relevant for nonlinear fiber optics, supercontinuum generation, rogue waves, and complex nonlinear dynamics. However, resonant radiation is narrowband, and the challenge is finding novel ways to generate and tailor broadband spectra. We theoretically predict that nonlinear self-accelerated pulses emit a novel form of synchrotron radiation that is extremely broadband and controllable. We develop an analytic theory and confirm the results by numerical analysis. This new form of supercontinuum generation can be highly engineered by shaping the trajectory of the nonlinear self-accelerated pulses. Our results may find applications in novel highly efficient classical and quantum sources for spectroscopy, biophysics, security, and metrology

Large-scale photonic natural language processing

Modern machine-learning applications require huge artificial networks demanding computational power and memory. Light-based platforms promise ultrafast and energy-efficient hardware, which may help realize next -generation data processing devices. However, current photonic networks are limited by the number of input-output nodes that can be processed in a single shot. This restricted network capacity prevents their application to relevant large-scale problems such as natural language processing. Here, we realize a photonic processor for supervised learning with a capacity exceeding 1.5 x 1010 optical nodes, more than one order of magnitude larger than any previous implementation, which enables photonic large-scale text encoding and classification. By exploiting the full three-dimensional structure of the optical field propagating in free space, we overcome the interpolation threshold and reach the over-parameterized region of machine learning, a condition that allows high-performance sentiment analysis with a minimal fraction of training points. Our results provide a novel sol-ution to scale up light-driven computing and open the route to photonic natural language processin

An optical Ising spin glass simulator with tuneable short range couplings

Non-deterministic polynomial-time (NP) problems are ubiquitous in almost every field of study. Recently, all-optical approaches have been explored for solving classic NP problems based on the spin-glass Ising Hamiltonian. However, obtaining programmable spin-couplings in large-scale optical Ising simulators, on the other hand, remains challenging. Here, we demonstrate control of the interaction length between user-defined parts of a fully-connected Ising system. This is achieved by exploiting the knowledge of the transmission matrix of a random medium and by using diffusers of various thickness. Finally, we exploit our spin-coupling control to observe replica-to-replica fluctuations and its analogy to standard replica symmetry breaking.Comment: arXiv admin note: text overlap with arXiv:2111.0789

Observation of replica symmetry breaking in disordered nonlinear wave propagation

A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symmetry breaking has been predicted in nonlinear wave propagation, including Bose-Einstein condensates and optics, but it has never been observed. Here, we report the experimental evidence of replica symmetry breaking in optical wave propagation, a phenomenon that emerges from the interplay of disorder and nonlinearity. When mode interaction dominates light dynamics in a disordered optical waveguide, different experimental realizations are found to have an anomalous overlap intensity distribution that signals a transition to an optical glassy phase. The findings demonstrate that nonlinear propagation can manifest features typical of spin-glasses and provide a novel platform for testing so-far unexplored fundamental physical theories for complex systems

Aging solitons in photorefractive dipolar glasses

We study experimentally the aging of optical spatial solitons in a dipolar glass hosted by a nanodisordered sample of photorefractive potassium-sodium-tantalate-niobate (KNTN). As the system ages, the waves erratically explore varying strengths of the nonlinear response, causing them to break up and scatter. We show that this process can still lead to solitons, but in a generalized form for which the changing response is compensated by changing the normalized wave size and intensity so as to maintain fixed the optical waveform