arXiv subjects

Natalia G. Berloff

Publications and source records attributed to Natalia G. Berloff.

At least 37 records · Page 2Linked to original sources

arXiv2024

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.

quant-ph↗

arXiv2024

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.

stat.CO↗

arXiv2024

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 of 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 analog all-optical degenerative diffusion models of machine learning to overcome the digital limitations of such models in processing speed and energy consumption.

quant-ph↗

arXiv2023

Analog Iterative Machine (AIM): using light to solve quadratic optimization problems with mixed variables

Solving optimization problems is challenging for existing digital computers and even for future quantum hardware. The practical importance of diverse problems, from healthcare to financial optimization, has driven the emergence of specialised hardware over the past decade. However, their support for problems with only binary variables severely restricts the scope of practical problems that can be efficiently embedded. We build analog iterative machine (AIM), the first instance of an opto-electronic solver that natively implements a wider class of quadratic unconstrained mixed optimization (QUMO) problems and supports all-to-all connectivity of both continuous and binary variables.Beyond synthetic 7-bit problems at small-scale, AIM solves the financial transaction settlement problem entirely in analog domain with higher accuracy than quantum hardware and at room temperature. With compute-in-memory operation and spatial-division multiplexed representation of variables, the design of AIM paves the path to chip-scale architecture with 100 times speed-up per unit-power over the latest GPUs for solving problems with 10,000 variables. The robustness of the AIM algorithm at such scale is further demonstrated by comparing it with commercial production solvers across multiple benchmarks, where for several problems we report new best solutions. By combining the superior QUMO abstraction, sophisticated gradient descent methods inspired by machine learning, and commodity hardware, AIM introduces a novel platform with a step change in expressiveness, performance, and scalability, for optimization in the post-Moores law era.

cs.ET↗

arXiv2023

Analog Photonics Computing for Information Processing, Inference and Optimisation

This review presents an overview of the current state-of-the-art in photonics computing, which leverages photons, photons coupled with matter, and optics-related technologies for effective and efficient computational purposes. It covers the history and development of photonics computing and modern analogue computing platforms and architectures, focusing on optimization tasks and neural network implementations. The authors examine special-purpose optimizers, mathematical descriptions of photonics optimizers, and their various interconnections. Disparate applications are discussed, including direct encoding, logistics, finance, phase retrieval, machine learning, neural networks, probabilistic graphical models, and image processing, among many others. The main directions of technological advancement and associated challenges in photonics computing are explored, along with an assessment of its efficiency. Finally, the paper discusses prospects and the field of optical quantum computing, providing insights into the potential applications of this technology.

physics.optics↗

arXiv2022

Physics-Enhanced Bifurcation Optimisers: All You Need Is a Canonical Complex Network

Many physical systems with the dynamical evolution that at its steady state gives a solution to optimization problems were proposed and realized as promising alternatives to conventional computing. Systems of oscillators such as coherent Ising and XY machines based on lasers, optical parametric oscillators, memristors, polariton and photon condensates are particularly promising due to their scalability, low power consumption and room temperature operation. They achieve a solution via the bifurcation of the fundamental supermode that globally minimizes either the power dissipation of the system or the system Hamiltonian. We show that the canonical Andronov-Hopf networks can capture the bifurcation behaviour of the physical optimizer. Furthermore, a continuous change of variables transforms any physical optimizer into the canonical network so that the success of the physical XY-Ising machine depends primarily on how well the parameters of the networks can be controlled. Our work, therefore, places different physical optimizers in the same mathematical framework that allows for the hybridization of ideas across disparate physical platforms.

nlin.CD↗

arXiv2022

Complex matter field universal models with optimal scaling for solving combinatorial optimization problems

We develop a universal model based on the classical complex matter fields that allow the optimal mapping of many real-life NP-hard combinatorial optimisation problems into the problem of minimising a spin Hamiltonian. We explicitly formulate one-to-one mapping for three famous problems: graph colouring, the travelling salesman, and the modular N-queens problem. We show that such a formulation allows for several orders of magnitude improvement in the search for the global minimum compared to the standard Ising formulation. At the same time, the amplitude dynamics escape from the local minima.

cond-mat.stat-mech↗

arXiv2021

Quantized Vortices Mediated Annealing

The complex matter-field lattice model is a ubiquitous and universal physics model that directly links to many universal spin models. However, finding the ground state of such a model for the most general interactions between the lattice sites is an NP-hard problem. The knowledge of the ground state is crucially essential for the range of applications from quantum annealing to predicting new materials and understanding the behaviour of spin glasses. Here we show how letting the quantised quasi-3D vortex loops pass through the system during the dissipative quench dynamics helps it find its ground state. Such quantized vortices mediated annealing (QVMA) is achieved by introducing and dynamically changing selected couplings between the lattice sites that either affect the local dimensionality of the medium or change the local mobility of the defects. Analysing the performance of QVMA on strongly glassy systems, we demonstrate that QVMA represents a highly efficient mode of physics enhanced computation.

cond-mat.dis-nn↗

arXiv2021

Geometric frustration in polygons of polariton condensates creating vortices of varying topological charge

Vorticity is a key ingredient to a broad variety of fluid phenomena, and its quantised version is considered to be the hallmark of superfluidity. Circulating flows that correspond to vortices of a large topological charge, termed giant vortices, are notoriously difficult to realise and even when externally imprinted, they are unstable, breaking into many vortices of a single charge. In spite of many theoretical proposals on the formation and stabilisation of giant vortices in ultra-cold atomic Bose-Einstein condensates and other superfluid systems, their experimental realisation remains elusive. Polariton condensates stand out from other superfluid systems due to their particularly strong interparticle interactions combined with their non-equilibrium nature, and as such provide an alternative testbed for the study of vortices. Here, we non-resonantly excite an odd number of polariton condensates at the vertices of a regular polygon and we observe the formation of a stable discrete vortex state with a large topological charge as a consequence of antibonding frustration between nearest neighbouring condensates.

cond-mat.mes-hall↗

arXiv2021

Emergence and Ordering of Polygonal Breathers in Polariton Condensates

We show that the simultaneous driving of a polariton condensate with both nonresonant and n^th order resonant pump frequencies allows for a generic mechanism of breather formation; from this, we construct for the second-order resonance a family of exotic breathers with nontrivial discrete order of rotational symmetry. Finally, we demonstrate the spontaneous emergence of both crystalline and glassy orderings of lattices of polygonal breathers, depending on the degree of polygonal excitations at the lattice sites.

cond-mat.mes-hall↗

arXiv2021

Large-scale Sustainable Search on Unconventional Computing Hardware

Since the advent of the Internet, quantifying the relative importance of web pages is at the core of search engine methods. According to one algorithm, PageRank, the worldwide web structure is represented by the Google matrix, whose principal eigenvector components assign a numerical value to web pages for their ranking. Finding such a dominant eigenvector on an ever-growing number of web pages becomes a computationally intensive task incompatible with Moore's Law. We demonstrate that special-purpose optical machines such as networks of optical parametric oscillators, lasers, and gain-dissipative condensates, may aid in accelerating the reliable reconstruction of principal eigenvectors of real-life web graphs. We discuss the feasibility of simulating the PageRank algorithm on large Google matrices using such unconventional hardware. We offer alternative rankings based on the minimisation of spin Hamiltonians. Our estimates show that special-purpose optical machines may provide dramatic improvements in power consumption over classical computing architectures.

cond-mat.dis-nn↗

arXiv2021

XY Neural Networks

The classical XY model is a lattice model of statistical mechanics notable for its universality in the rich hierarchy of the optical, laser and condensed matter systems. We show how to build complex structures for machine learning based on the XY model's nonlinear blocks. The final target is to reproduce the deep learning architectures, which can perform complicated tasks usually attributed to such architectures: speech recognition, visual processing, or other complex classification types with high quality. We developed the robust and transparent approach for the construction of such models, which has universal applicability (i.e. does not strongly connect to any particular physical system), allows many possible extensions while at the same time preserving the simplicity of the methodology.

physics.comp-ph↗

arXiv2020

Complexity continuum within Ising formulation of NP problems

A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for certain interaction matrix classes, yet not all problem instances are equivalently hard to optimise. We propose to identify computationally simple instances with an `optimisation simplicity criterion'. Such optimisation simplicity can be found for a wide range of models from spin glasses to k-regular maximum cut problems. Many optical, photonic, and electronic systems are neuromorphic architectures that can naturally operate to optimise problems satisfying this criterion and, therefore, such problems are often chosen to illustrate the computational advantages of new Ising machines. We further probe an intermediate complexity for sparse and dense models by analysing circulant coupling matrices, that can be `rewired' to introduce greater complexity. A compelling approach for distinguishing easy and hard instances within the same NP-hard class of problems can be a starting point in developing a standardised procedure for the performance evaluation of emerging physical simulators and physics-inspired algorithms.

quant-ph↗

arXiv2020

Multiply Charged Vortex States of Polariton Condensates

The existence of quantized vortices is a key feature of Bose-Einstein condensates. In equilibrium condensates only quantum vortices of unit topological charge are stable, due to the dynamical instabilities of multiply charged defects, unless supported by strong external rotation. Due to immense fundamental interest in the physics of these fundamental topological excitations, a great deal of work has been expended towards understanding ways to force their stability. Here we show that in photonic Bose-Einstein condensates of exciton-polariton quasiparticles pumped in an annular geometry, not only do the constant particle fluxes intrinsic to the system naturally stabilize multiply charged vortex states, but that such states can indeed form spontaneously during the condensate formation through a dynamical symmetry breaking mechanism. We elucidate the properties of these novel states, notably finding that they radiate acoustically, in a process analogous to the emission of gravitational waves from binary black holes. Finally, we show that the vorticity of these photonic fluids are fundamentally limited by a quantum Kelvin-Helmholtz instability, and therefore by the condensate radius and pumping intensity. This represents the first report of this instability - deeply fundamental in fluid dynamics - in a quantum photonic fluid.

nlin.PS↗

arXiv2020

Artificial polariton molecules

We show that geometrically coupled polariton condensates fabricated in semiconductor devices are versatile systems capable of simulating molecules with given characteristics. In particular, we consider oscillatory and stationary symmetric and asymmetric states in polariton dimers, trimers, and tetrads and their luminosity in real and Fourier space. The spectral weights of oscillatory states are associated with discrete spectral lines. Their number and separation can be controlled by changing the number and geometry of condensates, reflected by the coupling strengths. We also show that asymmetric stationary states combine discrete and continuous degrees of freedom in one system. The continuous degree of freedom is represented by the phase while the discrete degree of freedom is given by density asymmetry. Our work paves the way to engineer controllable artificial molecules with a range of properties manufactured on demand.

cond-mat.mes-hall↗

arXiv2020

Discrete Polynomial Optimization with Coherent Networks of Condensates and Complex Coupling Switching

Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation/coherence threshold have been recently proposed as efficient analog simulators of 2-local spin Hamiltonians with continuous or discrete degrees of freedom. We show that nonequilibrium condensates above the threshold arranged in an interacting network may realise k-local Hamiltonians with k>2 and lead to nontrivial phase configurations. The principle of the operation of such a system lays the ground for physics-inspired computing and the new efficient methods for finding solutions to the higher order binary optimization problems. We show how to facilitate the search for the global solution by invoking complex couplings in the system and demonstrate the efficiency of the method on tensors with million entries. This approach offers a highly flexible new kind of computation based on gain-dissipative simulators with complex coupling switching. g.

cond-mat.dis-nn↗

arXiv2020

Polaritonic XY-Ising Machine

Gain-dissipative systems of various physical origin have recently shown the ability to act as analogue minimisers of hard combinatorial optimisation problems. Whether or not these proposals will lead to any advantage in performance over the classical computations depends on the ability to establish controllable couplings for sufficiently dense short- and long-range interactions between the spins. Here, we propose a polaritonic XY-Ising machine based on a network of geometrically isolated polariton condensates capable of minimising discrete and continuous spin Hamiltonians. We elucidate the performance of the proposed computing platform for two types of couplings: relative and absolute. The interactions between the network nodes might be controlled by redirecting the emission between the condensates or by sending the phase information between nodes using resonant excitation. We discuss the conditions under which the proposed machine leads to a pure polariton simulator with pre-programmed couplings or results in a hybrid classical polariton simulator. We argue that the proposed architecture for the remote coupling control offers an improvement over geometrically coupled condensates in both accuracy and stability as well as increases versatility, range and connectivity of spin Hamiltonians that can be simulated with polariton networks.

cond-mat.mes-hall↗

arXiv2019

Nonlinear systems for unconventional computing

The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists and engineers. Many analogue physical systems including nonlinear oscillator networks, lasers, and condensates were proposed and realised to address hard computational problems from various areas of social and physical sciences and technology. The analogue systems emulate spin Hamiltonians with continuous or discrete degrees of freedom to which actual optimisation problems can be mapped. Understanding the underlying physical process by which the system finds the ground state often leads to new classes of system-inspired or quantum-inspired algorithms for hard optimisation. Together physical platforms and related algorithms can be combined to form a hybrid architecture that may one day compete with conventional computing. In this Chapter, we review some of the systems and physically-inspired algorithms that show such promise.

cs.ET↗