A biased Ising model using two coupled Kerr parametric oscillators with external force

TL;DR

This paper explores how an external force biases a network of coupled Kerr parametric oscillators, enabling control over Ising machine configurations and extending their capabilities beyond traditional spin systems.

Contribution

It introduces a method to control Ising machines with arbitrary bias using external forces, combining experimental and theoretical analysis of Kerr oscillator networks.

Findings

External force breaks phase-parity symmetry in Kerr oscillator networks.

Force can be used to control and bias the system's configuration.

The approach extends Ising machine capabilities beyond traditional spin systems.

Abstract

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 study such a network under the influence of an external force. The force breaks the collective phase-parity symmetry of the system and competes with the intrinsic coupling in ordering the network configuration, similar to how a magnetic field biases an interacting spin ensemble. Specifically, we demonstrate how the force can be used to control the system, and highlight the crucial role of the phase and symmetry of the force. Our work thereby provides a method to create Ising machines with arbitrary bias, extending even to exotic cases that are impossible to engineer in real spin systems.