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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16370 |
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| _version_ | 1866909604253794304 |
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| author | Morohoshi, Yuto Nakayama, Akimoto Manabe, Hidetaka Mitarai, Kosuke |
| author_facet | Morohoshi, Yuto Nakayama, Akimoto Manabe, Hidetaka Mitarai, Kosuke |
| contents | We propose a quantum machine learning task that is provably easy for quantum computers and arguably hard for classical ones. The task involves predicting quantities of the form $\mathrm{Tr}[f(H)ρ]$, where $f$ is an unknown function, given descriptions of $H$ and $ρ$. Using a Fourier-based feature map of Hamiltonians and linear regression, we theoretically establish the learnability of the task and implement it on a superconducting device using up to 40 qubits. This work provides a machine learning task with practical relevance, provable quantum easiness, and near-term feasibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning functions of Hamiltonians with Hamiltonian Fourier features Morohoshi, Yuto Nakayama, Akimoto Manabe, Hidetaka Mitarai, Kosuke Quantum Physics We propose a quantum machine learning task that is provably easy for quantum computers and arguably hard for classical ones. The task involves predicting quantities of the form $\mathrm{Tr}[f(H)ρ]$, where $f$ is an unknown function, given descriptions of $H$ and $ρ$. Using a Fourier-based feature map of Hamiltonians and linear regression, we theoretically establish the learnability of the task and implement it on a superconducting device using up to 40 qubits. This work provides a machine learning task with practical relevance, provable quantum easiness, and near-term feasibility. |
| title | Learning functions of Hamiltonians with Hamiltonian Fourier features |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.16370 |