Related papers: General Oscillator-Based Ising Machine Models with…
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of ``universal'' properties at the point of synchronization. Common biological systems of coupled…
The growing challenges of scaling digital computing motivate new approaches, especially through the dynamical evolution of physical systems that mimic neural networks and combinatorial optimization problems. While light is a hyper efficient…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Several continuous dynamical systems have recently been proposed as special-purpose analog computers designed to solve combinatorial optimization problems such as $k$-SAT or the Ising problem. While combinatorial optimization problems are…
Nature-inspired computation is receiving increasing attention. Various Ising machine implementations have recently been proven to be effective in solving numerous combinatorial optimization problems including maximum cut, low density parity…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…
Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a…
We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising…
Ising machines have attracted attention as efficient solvers for combinatorial optimization problems, which are formulated as ground-state (lowest-energy) search problems of the Ising model. Due to the limited bit-width of coefficients on…
An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
We present a comprehensive numerical study of dynamic phase transitions in the two-dimensional kinetic Ising model under a non-antisymmetric time-dependent magnetic field including a sinusoidal term and a second harmonic component. We…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions,…
We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective…