Phase-space negativity as a computational resource for quantum kernel methods

• URL: http://arxiv.org/abs/2405.12378v2
• Date: Wed, 06 Nov 2024 08:55:01 GMT
• Title: Phase-space negativity as a computational resource for quantum kernel methods
• Authors: Ulysse Chabaud, Roohollah Ghobadi, Salman Beigi, Saleh Rahimi-Keshari,
• Abstract summary: Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. We provide sufficient conditions for the efficient classical estimation of quantum kernel functions for bosonic systems. Our results underpin the role of the negativity in phase-space quasi-probability distributions as an essential resource in quantum machine learning.
• Score: 2.5499055723658097
• License:
• Abstract: Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device while the rest of computation is performed classically. Quantum advantages may be achieved through this method only if the quantum kernel function cannot be estimated efficiently on a classical computer. In this paper, we provide sufficient conditions for the efficient classical estimation of quantum kernel functions for bosonic systems. These conditions are based on phase-space properties of data-encoding quantum states associated with the quantum kernels: negative volume, non-classical depth, and excess range, which are shown to be three signatures of phase-space negativity. We consider quantum optical examples involving linear-optical networks with and without adaptive non-Gaussian measurements, and investigate the effects of loss on the efficiency of the classical simulation. Our results underpin the role of the negativity in phase-space quasi-probability distributions as an essential resource in quantum machine learning based on kernel methods.

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