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arXiv · 2504.16370

Learning functions of Hamiltonians with Hamiltonian Fourier features

Yuto Morohoshi·Akimoto Nakayama·Hidetaka Manabe·Kosuke Mitarai
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Abstract

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 $\mathrm{Tr}[f(H)\rho]$, where $f$ is an unknown function, given descriptions of $H$ and $\rho$. 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.

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Yuto Morohoshi, Akimoto Nakayama, Hidetaka Manabe, Kosuke Mitarai. 2025-04-23. Learning functions of Hamiltonians with Hamiltonian Fourier features. https://arxiv.org/abs/2504.16370

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