arXiv subjects

Claudio Conti

Publications and source records attributed to Claudio Conti.

At least 19 recordsLinked to original sources

arXiv2026

Complex Hyperspin Machine and Symmetry Quenching: Benchmark and scaling up to millions of degrees of freedom

Driven-dissipative oscillator networks have been proposed to simulate spin models on physical hardware, mostly focusing on systems of binary (Ising) spins, or systems of spin vectors in low dimensions. The equalized hyperspin machine was recently introduced to provide a single platform to simulate general models of $N$ coupled spin vectors with tunable dimension $D$, realizing dynamical annealing protocols to vary the spin dimensionality in time. These schemes are limited to real spins coupled via real coupling matrices. We propose a generalization of the hyperspin machine that works with complex fields and deals with complex Hermitian coupling matrices, implementing an amplitude equalization scheme. This system, which we name complex hyperspin machine, can work on optimization problems with complex valued hyperspins that can be cast on complex $D$-vector Hamiltonians. We benchmark the machine against a differential evolution (DE) algorithm on complex $D=2$ hyperspins up to $N=80$, showing that the fraction of instances where a lower-energy solution is found grows with system size and coupling density, reaching $92.5\%$ at the largest considered sizes. When the DE finds a lower-energy solution, the machine still reaches a median relative energy deviation that lies between $10^{-15}$ and $10^{-12}$ while running at substantially lower computational cost. Using the complex nature of the field, we introduce a new dimensional reduction protocol that we name symmetry quenching, which collapses complex variables that map to XY spins onto real Ising spins by switching on the parametric pump. We show on Max-Cut instances with known ground states that symmetry quenching outperforms a fixed-pump Ising machine, reaching exact ground states in the presence of equalization. We scale the system to $N=10^6$ hyperspins, or $8\times10^6$ dynamical variables, on a Hermitian sparse two-dimensional lattice.

physics.comp-ph↗

arXiv2026

Experimental Demonstration of 7-Dimensional N-Vector Model with Dimensional Inflation and Annealing

We report the first experimental realization of a physical system described by a high-dimensional Hamiltonian comprising up to seven dimensions. Our setup is based on a holographic optical computer, which realizes a dimensional inflation by spatial and temporal multiplexing of lower dimensional systems. We demonstrate an $N$-vector model, with applications in field theory and computing. The approach is scalable and enables table-top implementation of high-dimensional theoretical models, and novel methods for combinatorial optimization. We experimentally demonstrate dimensional annealing: by dynamically reducing the number of dimensions, the ground state of an Ising model is found in complex graphs by an adiabatic evolution from high-dimensional spaces.

physics.optics↗

arXiv2026

Nonlinear Spectral Computing

Many machine learning algorithms rely on the Fourier transform, which is also the inner core of many analog computing devices and, specifically, of optical computing. The square of the modulus of the Fourier spectrum naturally maps onto pairwise interactions, as in the renowned Ising model, making it applicable to combinatorial optimization. Here we show how the nonlinear Fourier transform, related to integrable nonlinear partial differential equations, significantly widens the computational capability and also enables a wide variety of computing gates. We study specifically the case of the nonlinear Schrödinger equation; we introduce an input composed by ``tokens'', i.e., batches of information encoded in a multi-step potential, and we show how the nonlinear spectral computing arising in the wave propagation not only generalizes combinatorial optimization to higher order problems, but also realizes boolean gates. In the weakly nonlinear regime, nonlinearity generates higher-order interactions as perturbative corrections to the pairwise terms. In the solitonic regime, the discrete nonlinear spectrum performs digital computation through soliton generation. By using four input tokens, we demonstrate the programmability of all 256 Boolean functions of three variables, including 3-SAT instances. Our results show that integrable nonlinear propagation provides an unprecedented single physical platform for higher-order and logical computation, opening the way to a rich variety of new algorithms for analog computing, machine learning, and classical and quantum information processing.

nlin.SI↗

arXiv2026

On-shell renormalization of sine-Gordon by the quantum inverse scattering method

In the quantum inverse scattering method, the sine-Gordon model is solved on a lattice, and its continuum and infinite-volume limits become uniform only after the length of the box is rescaled. We show that this rescaling, supplemented by an on-shell condition, defines a renormalization scheme. The whole dependence on the cut-off is absorbed into a factor $Z_L$ multiplying the length of the box, with an exponent fixed by the scaling dimension of the vertex operator; neither the field nor the coupling $β$ is renormalized, no subtraction scale is introduced, and the mass parameter receives a finite renormalization, fixed by requiring that the lightest breather has the mass of the boson in the linearized theory. The soliton and breather masses follow from the eigenvalues of the monodromy operator as functions of parameters that do not run, and reduce to the classical and semiclassical results as $β\rightarrow0$. In particular, the mass ratios are produced directly from the regularized construction, while the relation between the lattice parameters and the physical scale is absorbed into $Z_L$ and never needs to be computed. The scheme is a reparameterization of the theory which makes explicit the interplay between integrability and renormalization. We compare it with Coleman's normal ordering and with conformal perturbation theory, and we argue that it extends to ultralocal integrable theories with a massive spectrum, possibly including asymptotically free models that admit an ultralocal lattice regularization.

hep-th↗

arXiv2026

Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines

Equilibrium Propagation offers a compelling alternative to traditional machine learning for training energy-based networks. Here we demonstrate a hybrid optical-digital implementation of EP using a Spatial Photonic Ising Machine (SPIM). The SPIM exploits the gauge transformation method to optically encode both continuous neuron states and rank-1 binary trainable patterns as phase modulations via a spatial light modulator, with inference realized using a finite difference scheme. The experimental system is evaluated on the Wine classification dataset. The potential of this approach, including the use of continuous couplings and structured coupling matrices, is evaluated numerically on the more complex MNIST dataset. Our work provides a concrete pathway toward energy-efficient physical implementations of Equilibrium Propagation.

physics.optics↗

arXiv2026

Ising selector machine by Kerr parametric oscillators

Ising machines are physical platforms designed to minimize the energy of classical Ising Hamiltonians, yet accessing specific excited states remains an open challenge of both fundamental and practical relevance. In this letter we show that a network of Kerr parametric oscillators (KPOs) naturally implements an Ising selector machine. By tuning the frequency detuning between the parametric pump and the oscillator resonances, the system can be steered to converge close to the ground state, the highest-energy configuration, or targeted intermediate excited states. Beyond mean field, numerical simulations based on the truncated Wigner approximation demonstrate that noise insertion preserves the energetic structure of the landscape. The targeted state emerges with an exponentially enhanced probability over the rest of the Ising spectrum. Our results establish the pump-cavity detuning as a control knob for navigating the full Ising energy landscape, opening a route to applications in Boltzmann sampling, hardness characterization, and spectral analysis of combinatorial problems.

quant-ph↗

arXiv2026

Realistic prospects for testing a relativistic local quantum measurement inequality

We investigate the experimental prospects for testing a relativistic local quantum measurement inequality that quantifies the trade-off between vacuum insensitivity and responsiveness to excitations for finite-size detectors. Building on the Reeh--Schlieder approximation for coherent states, we derive an explicit and practically applicable bound for arbitrary coherent states. To connect with realistic photodetection scenarios, we model the detection region as a square prism operating over a finite time window and consider a normally incident single-mode coherent state. Numerical results exhibit the expected qualitative behavior: suppressing dark counts necessarily tightens the achievable click probability.

quant-ph↗

arXiv2025

Holonomic multi-controlled gates for single-photon states

Controlled and multi-controlled quantum gates, whose action on a target qubit depends on the state of multiple control qubits, represent a fundamental logical building block for complex quantum algorithms. We propose a scheme for realizing this class of gates based on non-Abelian holonomies in modulated photonic waveguide networks. Our approach relies on linear photonic cicuits formed by two star networks coupled via a two-path circuit. A star network with M peripheral waveguides coupled to a single central site, or M-pod, naturally generalizes the tripod structure used in non-Abelian Thouless pumping and stimulated Raman adiabatic passage (STIRAP). In the present work, we first analyze the minimal case of two connected tripods and design adiabatic driving loops that implement single-qubit, CNOT, and SWAP gates. We then show how extending the approach to larger M-pod structures enables the realization of multiply controlled operations, which we exemplify by designing Toffoli and the OR gate on two coupled pentapods. Finally, we demonstrate that networks of connected tripods can implement the Deutsch quantum query algorithm.

quant-ph↗

arXiv2025

Fast and length-independent transport time supported by topological edge states in finite-size Su-Schrieffer-Heeger chains

In order to transport information with topological protection, we explore experimentally the fast transport time using edge states in one-dimensional Su-Schrieffer-Heeger (SSH) chains. The transport time is investigated in both one- and two-dimensional models with topological non-trivial band structures. The fast transport is inherited with the wavefunction localization, giving a stronger effective coupling strength between the mode and the measurement leads. Also the transport time in one-dimension is independent of the system size. To verify the asertion, we implement a chain of split-ring resonators and their complementary ones with controllable hopping strengths. By performing the measurements on the group delay of non-trivially topological edge states with pulse excitations, the transport time between two edge states is directly observed with the chain length up to $20$. Along the route to harness topology to protect optical information, our experimental demonstrations provide a crucial guideline for utilizing photonic topological devices.

physics.optics↗

arXiv2025

Thouless quantum walks in topological flat bands

Non-Abelian gauge symmetries are cornerstones of modern theoretical physics, underlying fundamental interactions and the geometric structure of quantum mechanics. However, their potential to control quantum coherence, entangle- ment, and transport in engineered quantum systems remains to a large extent unexplored. In this work, we propose utilizing non-Abelian Thouless pumping to realize one-dimensional discrete-time quantum walks on topological lattices char- acterized by degenerate flat bands. Through carefully designed pumping cycles, we implement different classes of holonomic coin and shift operators. This frame- work allows for the construction of quantum walks that encode the topological and geometric properties of the underlying system. Remarkably, the resulting evolution exhibits parity symmetry breaking and gives rise to a dynamical pro- cess governed by a Weyl-like equation, highlighting the deep connection between parity and time-reversal symmetry breaking in the system.

cond-mat.mes-hall↗

arXiv2025

An inequality for relativistic local quantum measurements

We investigate the trade-off between vacuum insensitivity and sensitivity to excitations in finite-size detectors, taking measurement locality as a fundamental constraint. We derive an upper bound on the detectability of vacuum excitation, given a small but nonzero probability of false positives in the vacuum state. The result is independent of the specific details of the measurement or the underlying physical mechanisms of the detector and relies only on the assumption of locality. Experimental confirmation or violation of the inequality would provide a test of the axioms of algebraic quantum field theory, offer new insights into the measurement problem in relativistic quantum physics, and establish a fundamental technological limit in local particle detection.

quant-ph↗

arXiv2025

Reeh-Schlieder approximation for coherent states

We present an explicit, fully local Reeh-Schlieder approximation scheme for coherent states of a free scalar field. For any bounded region $\mathcal{U}$, we construct a one-parameter family of bounded operators $\hat{A}_ζ$ localized in the causal complement of $\mathcal{U}$. The action of $\hat{A}_ζ$ on the vacuum approximates the target coherent state in the limit $ζ\to 0$.

math-ph↗

arXiv2025

Particle trajectories in light pulse spacetime

In our previous work (Phys. Rev. Research 7, 033079), we derived the metric tensor for cylindrically shaped pulses with uniform energy density. Building upon that framework, we derive the complete set of geodesics with zero angular velocity. We show that perturbations in particle trajectories may be observed in gamma ray bursts. Also, deviations in the motion of moving particles are significantly larger than those previously found for particles that are initially at rest.

gr-qc↗

arXiv2025

Equalized Hyperspin Machine

The reliable simulation of spin models is of critical importance to tackle complex optimization problems that are intractable on conventional computing machines. The recently introduced hyperspin machine, which is a network of linearly and nonlinearly coupled parametric oscillators, provides a versatile simulator of general classical vector spin models in arbitrary dimension, finding the minimum of the simulated spin Hamiltonian and implementing novel annealing algorithms. In the hyperspin machine, oscillators evolve in time minimizing a cost function that must resemble the desired spin Hamiltonian in order for the system to reliably simulate the target spin model. This condition is met if the hyperspin amplitudes are equal in the steady state. Currently, no mechanism to enforce equal amplitudes exists. Here, we bridge this gap and introduce a method to simulate the hyperspin machine with equalized amplitudes in the steady state. We employ an additional network of oscillators (named equalizers) that connect to the hyperspin machine via an antisymmetric nonlinear coupling and equalize the hyperspin amplitudes. We demonstrate the performance of such an equalized hyperspin machine by large-scale numerical simulations up to $10000$ hyperspins. Compared to the hyperspin machine without equalization, we find that the equalized hyperspin machine (i) Reaches orders of magnitude lower spin energy, and (ii) Its performance is significantly less sensitive to the system parameters. The equalized hyperspin machine offers a competitive spin Hamiltonian minimizer and opens the possibility to combine amplitude equalization with complex annealing protocols to further boost the performance of spin machines.

physics.comp-ph↗

arXiv2025

Analyzing partially-polarized light with a photonic deep random neural network

Optical neural networks are emerging as a powerful and versatile tool for processing optical signals directly in the optical domain with superior speed, integrability, and functionality. Their application to optical polarization enables neuromorphic polarization sensors, but their operation is limited to fully-polarized light. Here, we demonstrate single-shot analysis of partially-polarized beams with a photonic random neural network (PRNN). The PRNN is composed of a series of optical layers implemented by a stack of scattering media and a few trainable digital nodes. The setup infers the degree-of-polarization and the Stokes parameters of the polarized component with precision comparable to off-the-shelf polarimeters. The use of several optical layers allows to enhance the accuracy, reduce the sensor size, and minimize digital costs, demonstrating the advantage of a deep optical encoder for processing polarization information. Our results point out photonic neural networks as fast, compact, broadband, low-cost polarimeters that are widely applicable from sensing to imaging.

physics.optics↗

arXiv2025

Phase Retrieval via Gain-Based Photonic XY-Hamiltonian Optimization

Phase-retrieval from coded diffraction patterns (CDP) is important to X-ray crystallography, diffraction tomography and astronomical imaging, yet remains a hard, non-convex inverse problem. We show that CDP recovery can be reformulated exactly as the minimisation of a continuous-variable XY Hamiltonian and solved by gain-based photonic networks. The coupled-mode equations we exploit are the natural mean-field dynamics of exciton-polariton condensate lattices, coupled-laser arrays and driven photon Bose-Einstein condensates, while other hardware such as the spatial photonic Ising machine can implement the same update rule through high-speed digital feedback, preserving full optical parallelism. Numerical experiments on images, two- and three-dimensional vortices and unstructured complex data demonstrate that the gain-based solver consistently outperforms the state-of-the-art Relaxed-Reflect-Reflect (RRR) algorithm in the medium-noise regime (signal-to-noise ratios 10--40 dB) and retains this advantage as problem size scales. Because the physical platform performs the continuous optimisation, our approach promises fast, energy-efficient phase retrieval on readily available photonic hardware. uch as two- and three-dimensional vortices, and unstructured random data. Moreover, the solver's accuracy remains high as problem sizes increase, underscoring its scalability.

physics.optics↗

arXiv2025

Second-order nonlinear disordered photonic media

The field of complex photonics has garnered significant interest due to its rich physics and myriad applications spanning physics, engineering, biology, and medicine. However, a substantial portion of research focuses primarily on the linear medium. Over the years, optical nonlinearity, particularly the second order denoted as $χ^{(2)}$, has been harnessed for diverse applications such as frequency conversions, three-wave mixing, material characterizations, and bio-imaging. When $χ^{(2)}$-nonlinearity combines with the disorder, a new realm of physics emerges, which in the last 30 years has witnessed substantial progress in fundamental studies and futuristic applications. This review aims to explore fundamental concepts concerning $χ^{(2)}$-nonlinear disordered media, chart the field's evolution, highlight current interests within the research community, and conclude with a future perspective.

physics.optics↗

arXiv2025

Ising machine by dimensional collapse of nonlinear polarization oscillators

Ising machines show promise as ultrafast hardware for optimizations encoded in Ising Hamiltonians but fall short in terms of success rate and performance scaling. Here, we propose a novel Ising machine that exploits the three-dimensional nature of nonlinear polarization oscillators to counteract these limitations. Based on the evolution of the optical polarization in third-order nonlinear media, the high-dimensional machine reaches the Ising ground state by the mechanism of dimensional collapse: the dynamics on the Poincaré sphere undergoes a self-induced collapse into polarization fixed points mapping Ising spins. The photonic setup consists of polarization-modulated pulses in a $χ^{(3)}$ crystal subject to iterative feedback. We numerically demonstrate that its high-dimensional operation leads to an enhanced success probability on benchmark graphs and an exponential improvement in performance scaling with respect to coherent Ising machines. The proposed polarization Ising machine paves the way for a new class of Ising solvers with enhanced computing capabilities.

physics.optics↗