Dawn and fall of non-Gaussianity in the quantum parametric oscillator

Abstract

Systems of coupled optical parametric oscillators (OPOs) forming an Ising machine are emerging as large-scale simulators of the Ising model. The advances in computer science and nonlinear optics have triggered not only the physical realization of hybrid (electro-optical) or all-optical Ising machines, but also the demonstration of quantum-inspired algorithms boosting their performances. To date, the use of the quantum nature of parametrically generated light as a further resource for computation represents a major open issue. A key quantum feature is the non-Gaussian character of the system state across the oscillation threshold. In this paper, we perform an extensive analysis of the emergence of non-Gaussianity in the single quantum OPO with an applied external field. We model the OPO by a Lindblad master equation, which is numerically solved by an ab initio method based on exact diagonalization. Non-Gaussianity is quantified by means of three different metrics: Hilbert-Schmidt distance, quantum relative entropy, and photon distribution. Our findings reveal a nontrivial interplay between parametric drive and applied field: (i) Increasing pump monotonously enhances non-Gaussianity, and (ii) Increasing field first sharpens non-Gaussianity, and then restores the Gaussian character of the state when above a threshold value.

10 pages, 4 figures

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• The physics of optical computing
• Non-Gaussian Quantum States and Where to Find Them
• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• A measure of the non-Gaussian character of a quantum state
• Coherent Ising machines -- Quantum optics and neural network perspectives
• A Quantum Model for Coherent Ising Machines: Discrete-time Measurement Feedback Formulation
• Can nonlinear parametric oscillators solve random Ising models?
• Coherent Ising machines with error correction feedback
• All-optical scalable spatial coherent Ising machine
• Microwave photon detection at parametric criticality
• Multidimensional hyperspin machine
• Coherent dynamics in frustrated coupled parametric oscillators
• Hyperscaling in the coherent hyperspin machine

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