Related papers: Theory of coupled parametric oscillators beyond co…
Ising machines, hardware accelerators for combinatorial optimization and probabilistic sampling problems, have gained significant interest recently. A key element is stochasticity, which enables a wide exploration of configurations, thereby…
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…
We analyze the static and dynamical properties of two Ising-coupled quantum spins embedded in a common bosonic bath as an archetype of dissipative quantum mechanics. First, we elucidate the ground state phase diagram for an ohmic and 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…
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…
The Coherent Ising Machine (CIM) is a non-conventional architecture that takes inspiration from physical annealing processes to solve Ising problems heuristically. Its dynamics are naturally continuous and described by a set of ordinary…
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:…
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…
I present a theoretical treatment of parametric scattering in strong coupling semiconductor microcavities to model experiments in which parametric oscillator behaviour has been observed. The model consists of a non-linear excitonic…
A promising paradigm of quantum computing for achieving practical quantum advantages is quantum annealing or quantum approximate optimization algorithm, where the classical problems are encoded in Ising interactions. However, it is…
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 present a new scheme to efficiently establish entanglement between optical modes in a time-multiplexed coherent Ising machine (CIM) by means of nonlocal measurement and feedback. We numerically simulate and evaluate the generation of…
Polarisation effects in the microcavity parametric oscillator are studied using a simple model in which two chi-three optical parametric oscillators are coupled together. It is found that there are, in general, a number of steady states of…
We propose two schemes to generate entanglement between a pair of mechanical oscillators using parametric amplification. In contrast to existing parametric drive-based protocols, both schemes operate in the steady-state. Using a detuned…
The Hamiltonian for a PT-symmetric chain of coupled oscillators is constructed. It is shown that if the loss-gain parameter $\gamma$ is uniform for all oscillators, then as the number of oscillators increases, the region of unbroken…
What is the fate of an oscillator when its inductance and capacitance are varied while its frequency is kept constant? Inspired by this question, we propose a protocol to implement parity-time (PT) symmetry in a lone oscillator. Different…
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator…
We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum…
Ising machines (IMs) are specialized devices designed to efficiently solve combinatorial optimization problems (COPs). They consist of artificial spins that evolve towards a low-energy configuration representing a problem's solution. Most…
In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…