Related papers: Controlled asymmetric Ising model implemented with…
Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin…
We study simultaneous parametric oscillations in a system composed of two distributed-element-circuit Josephson parametric oscillators in the single-photon Kerr regime coupled via a static capacitance. The energy of the system is described…
Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to…
In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. The controlling parameters are the…
The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically-driven circuits of stochastic binary resistors with memory. A key feature of our…
Networks of coupled Kerr parametric oscillators (KPOs) are a leading physical platform for analog solving of complex optimization problems. These systems are colloquially known as ``Ising machines''. We experimentally and theoretically…
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…
We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry…
We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate…
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…
Parametric couplings in engineered quantum systems are a powerful tool to control, manipulate and enhance interactions in a variety of platforms. It allows us to bring systems of different energy scales into communication with each other.…
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent…
We find an unexpected phenomenon of coherently synchronized oscillations in a mirror-symmetric many-body localized system. A synchronization transition of the spin oscillations is found by changing the spin-spin interactions. To understand…
Solving intractable mathematical problems in simulators composed of atoms, ions, photons or electrons has recently emerged as a subject of intense interest. Here we extend this concept to phonons that are localised in spectrally pure…
Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…