Effective spin models of Kerr-nonlinear parametric oscillators for quantum annealing

TL;DR

This paper develops effective spin models for Kerr-nonlinear parametric oscillators to better understand their use in quantum annealing, bridging bosonic and spin frameworks.

Contribution

It introduces a novel spin model representation of KPOs using a Holstein-Primakoff transformation, enabling analysis within the conventional QA framework.

Findings

Spin models qualitatively reproduce KPO behavior.

Effective models map physical parameters to spin terms.

Models work well for large spin values and tuned parameters.

Abstract

A method of quantum annealing (QA) using Kerr-nonlinear parametric oscillators (KPOs) was proposed. This method is described by bosonic operators and has different characteristics from QA based on the transverse-field Ising model. As the first step to describe this method in the conventional framework of QA, we propose effective spin models of KPOs. The spin models are obtained via a variant of the Holstein-Primakoff transformation and are described by spin-$s$ operators. The terms for detuning, coherent driving, parametric driving, and the Kerr effect are mapped to the transverse field, longitudinal field, nonlinear terms for the z- and x-components of spins, respectively. By analyzing the spin models corresponding to KPOs in several settings, we demonstrate that the present spin models for a rather large $s$ and tuned parameters qualitatively reproduce behavior of KPOs.