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Coupled Kerr parametric oscillators (KPOs) are a promising resource for classical and quantum analog computation, for example to find the ground state of Ising Hamiltonians. Yet, the state space of strongly coupled KPO networks is very…
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…
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…
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…
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 -…
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…
Networks of coupled Kerr parametric oscillators (KPOs) hold promise as for the realization of neuromorphic and quantum computation. Yet, their rich bifurcation structure remains largely not understood. Here, we employ secular perturbation…
The vision of building computational hardware for problem optimization has spurred large efforts in the physics community. In particular, networks of Kerr parametric oscillators (KPOs) are envisioned as simulators for finding the ground…
Coupled resonators form band-like optical states that support rich nonlinearities beyond what is possible in single resonators. In these systems, four-wave mixing mediates interband coupling, displaying multimode dynamics that span both…
We consider a model of two harmonically driven damped harmonic oscillators that are coupled linearly and with a cross-Kerr coupling. We show how to distinguish this combination of coupling types from the case where a coupling of…
Time-multiplexed networks of degenerate optical parametric oscillators have demonstrated remarkable success in simulating coupled Ising spins, thus providing a promising route to solving complex combinatorial optimization problems. In these…
The nonlinear, parametric coupling between two harmonic oscillators has been used in the field of optomechanics for breakthrough experiments regarding the control and detection of mechanical resonators. Although this type of interaction is…
We theoretically present new unit circuits of Kerr parametric oscillators (KPOs) with four-body interactions, which enable the scalable embedding of all-to-all connected logical Ising spins using the Lechner-Hauke-Zoller (LHZ) scheme. These…
We propose a flexible scheme based on three coupled optical microcavities which permits to achieve stable oscillations in the microwave range, the frequency of which depends only on the cavity coupling rates. We find the different dynamical…
Coupled mechanical oscillations were first observed in paired pendulum clocks in the mid-seventeenth century and were extensively studied for their novel sympathetic oscillation dynamics. In this era of nanotechnologies, coupled…
We investigate the classical dynamics of optical nonlinear Kerr couplers, focusing on their potential relevance to quantum computing applications. The system consists of three Kerr-type nonlinear oscillators arranged in two configurations:…
Networks of coupled nonlinear oscillators are emerging as powerful physical platforms for implementing Ising machines. Yet the relationship between parametric-oscillator implementations and traditional oscillator-based Ising machines…
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.…
When the coupling rate between two quantum systems becomes as large as their characteristic frequencies, it induces dramatic effects on their dynamics and even on the nature of their ground state. The case of a qubit coupled to a harmonic…
The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are well understood in the regime of weak and intermediate Josephson coupling, i.e. E_J\lesssim E_C. Instead of perturbative treatment of charging effects, the…