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arXiv:2202.07160 · Physical Review A

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

Ryoji Miyazaki

Published Jun 29, 2022• 9 citations
arXivHTMLPDF

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, and 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 the behavior of KPOs.

DOI
10.1103/physreva.105.062457

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Quantum annealing (QA) is an algorithm to find the ground state of the problem Hamiltonian by using an adiabatic time evolution. An approach to evaluate adiabaticity in the experiment by applying spectroscopic techniques has recently been suggested. However, this method requires temporal oscillation of interaction strength during QA, posing challenges for experimental demonstration. Here, we propose an experimental method for evaluating adiabaticity when performing QA with a parametric oscillator with Kerr nonlinearity (KPO). Importantly, our proposal offers a significant advantage by eliminating the need for temporal oscillation of interactions during QA. We investigate its performance through numerical simulations, and we show the feasibility of our method.
Coherent states offer a promising path for near-term quantum computing due to their inherent protection against bit-flip noise. However, their large photon numbers can be challenging for numerical simulation. This paper introduces an effective model, representing coherent-state quantum annealing using spin-1/2 degrees of freedom. We demonstrate that this model yields accurate predictions for realistic experimental settings and can therefore serve as a practical tool for optimizing future quantum hardware.
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