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.

10 pages, 7 figures

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Cited by in corpus (7)

• The squeezed Kerr oscillator: spectral kissing and phase-flip robustness
• Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors
• Fast elementary gates for universal quantum computation with Kerr parametric oscillator qubits
• How to experimentally evaluate the adiabatic condition for quantum annealing
• Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Unraveling the switching dynamics in a quantum double-well potential
• Spin Model for Quantum Annealing with Kerr Parametric Oscillators