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

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.

Numerical gate synthesis for quantum heuristics on bosonic quantum processors

“…, where σ z are the standard Pauli matrices. For circuit quantum electrodynamics (cQED) systems, note also that there are ways to find effective spin models, which is generally used for encoding of quantum heuristic algorithms [13].…”