Phase-space negativity as a computational resource for quantum kernel methods
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912114906497024 |
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| author | Chabaud, Ulysse Ghobadi, Roohollah Beigi, Salman Rahimi-Keshari, Saleh |
| author_facet | Chabaud, Ulysse Ghobadi, Roohollah Beigi, Salman Rahimi-Keshari, Saleh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase-space negativity as a computational resource for quantum kernel methods Chabaud, Ulysse Ghobadi, Roohollah Beigi, Salman Rahimi-Keshari, Saleh Quantum Physics 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. |
| title | Phase-space negativity as a computational resource for quantum kernel methods |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.12378 |