Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Spin-Model Simulations for KPO Annealing

L. Stenzel

Published Feb 17, 2026• 1 citation
Publisher

Abstract

Code and data accompanying our paper arXiv:2603.11931 on effective spin-1/2 models for simulating quantum annealing in Kerr parametric oscillators (KPOs).
DOI
10.5281/zenodo.18671232

Related papers

Spin Model for Quantum Annealing with Kerr Parametric Oscillators

Leo Stenzel, Roeland ter Hoeven, Ryoji Miyazaki +3 more

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.

quant-pharXiv:2603.11931•Physical Review A•Mar 13, 2026•0 citations

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

Ryoji Miyazaki

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.

arXiv:2202.07160•Physical Review A•Jun 29, 2022•9 citations

Recent Progress in Quantum Annealing Machine Using Kerr-Parametric Oscillators

Aiko Yamaguchi

International Conference on Solid State Devices and Materials (SSDM)•Sep 28, 2022•0 citations

Quantum annealing in capacitively coupled Kerr parametric oscillators using frequency-chirped drives

T. Yamaji, S. Masuda, Y. Kano +7 more

We study parametric oscillations of two capacitively coupled Kerr parametric oscillators (KPOs) with frequency-chirped two- and one-photon drives. The two-KPO system adiabatically evolves from the initial vacuum state to an oscillation state corresponding to a solution state in quantum-annealing applications. Frequency chirping dynamically changes the detuning between resonance and oscillation frequencies during parametric modulation and reduces unwanted population transfer to excited states caused by pure dephasing and photon loss. We observe that frequency chirping increases the success probability to obtain the solution state and that simulations taking into account pure dephasing reproduce experiments with and without frequency chirping. This study demonstrates the effectiveness and applicability of frequency chirping to a KPO-based quantum annealer.

arXiv:2506.23539•Physical Review Applied•Dec 4, 2025•1 citation

Proposal to experimentally evaluate the adiabatic condition of quantum annealing in coupled systems of Kerr parametric oscillators

Yuichiro Mori, Harunobu Hiratsuka, Yuichiro Matsuzaki

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.

arXiv:2408.09363•Aug 18, 2024•0 citations

Optimal quantum annealing in p-spin model

Kostyantyn Kechedzhi, Vadim Smelyanskiy

Bulletin of the American Physical Society•Mar 4, 2015•0 citations
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.
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-sss 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 zzz and xxx 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 sss and tuned parameters qualitatively reproduce the behavior of KPOs.
We study parametric oscillations of two capacitively coupled Kerr parametric oscillators (KPOs) with frequency-chirped two- and one-photon drives. The two-KPO system adiabatically evolves from the initial vacuum state to an oscillation state corresponding to a solution state in quantum-annealing applications. Frequency chirping dynamically changes the detuning between resonance and oscillation frequencies during parametric modulation and reduces unwanted population transfer to excited states caused by pure dephasing and photon loss. We observe that frequency chirping increases the success probability to obtain the solution state and that simulations taking into account pure dephasing reproduce experiments with and without frequency chirping. This study demonstrates the effectiveness and applicability of frequency chirping to a KPO-based quantum annealer.
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.