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.

arXiv comment10 pages, 7 figures

References in corpus (35)

• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Adiabatic Quantum Computing
• Quantum Annealing and Analog Quantum Computation
• Perspectives of quantum annealing: Methods and implementations
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network: Toward quantum soft computing
• Bias-preserving gates with stabilized cat qubits
• Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators
• Quantum annealing with antiferromagnetic fluctuations
• Universal quantum computation with a nonlinear oscillator network
• Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators
• From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms
• Robust quantum optimizer with full connectivity
• Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
• Quantum dynamics of a few-photon parametric oscillator
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• Dissipative quantum bifurcation machine: Quantum heating of coupled nonlinear oscillators
• Interaction-induced time-symmetry breaking in driven quantum oscillators
• Role of Non-stoquastic Catalysts in Quantum Adiabatic Optimization
• A quantum annealer with fully programmable all-to-all coupling via Floquet engineering
• Preparing quasienergy states on demand: A parametric oscillator
• High-accuracy Ising machine using Kerr-nonlinear parametric oscillators with local four-body interactions
• Two-photon driven Kerr resonator for quantum annealing with three-dimensional circuit QED
• Stabilizing a Bosonic Qubit using Colored Dissipation
• Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Steering random spin systems to speed up the quantum adiabatic algorithm
• Quantum Correlations in the Kerr Ising Model
• Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
• Bifurcation-based quantum annealing with nested spins

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• Unraveling the switching dynamics in a quantum double-well potential
• Spin Model for Quantum Annealing with Kerr Parametric Oscillators