Advances in quantum information processing compel us to explore learning from quantum data . We consider a classical-quantum learning problem in which the samples are quantum states with classical labels and the predictors are quantum measurements . To study this problem , we introduce a quantum counterpart of PAC framework . We argue that the major difficulties arising from the quantum nature of the problem are the compatibility of the measurements and the no-cloning principle . With that in mind, we establish bounds on the quantum sample complexity for a family of quantum concept classes called concentrated measurements . Using a quantum Fourier expansion on qubits, we propose a quantum low-degree learning algorithm which is a quantum counterpart of (Linial et al., 1993) .
We study learning from quantum data , in particular quantum state classification which has applications, among others, in classifying the separability of quantum states. In this learning model, there are n quantum states with classical labels as the training samples. Predictors are quantum measurements that when applied to the next unseen quantum state predict its classical label. By integrating learning theory with quantum information , we introduce a quantum counterpart of the PAC framework for learning with respect to classes of measurements . We argue that major challenges arising from the quantum nature of the problem are measurement incompatibility and the no-cloning principle -- prohibiting sample reuse. Then, after introducing a Fourier expansion through Pauli's operators, we study learning with respect to an infinite class of quantum measurements whose operator's Fourier spectrum is concentrated on low degree terms. We propose a quantum learning algorithm and show that the quantum sample complexity depends on the ``compatibility structure" of such measurement classes -- the more compatible the class is, the lower the quantum sample complexity will be. We further introduce k-junta measurements as a special class of low-depth quantum circuits whose Fourier spectrum is concentrated on low degrees .
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Advances in quantum information processing compel us to explore
We study
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. We consider a classical-quantum learning problem in which the samples are
, in particular quantum state classification which has applications, among others, in classifying the separability of quantum states. In this learning model, there are n
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and the predictors
as the training samples. Predictors
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. To study this problem
that when applied to the next unseen quantum state predict its classical label. By integrating learning theory with quantum information
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PAC framework
the PAC framework for learning with respect to classes of measurements
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the major difficulties
major challenges
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the compatibility of the measurements
measurement incompatibility
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. With that in mind, we establish bounds on the quantum sample complexity for a family of quantum concept classes called concentrated measurements . Using a quantum Fourier expansion on qubits, we
-- prohibiting sample reuse. Then, after introducing a Fourier expansion through Pauli's operators, we study learning with respect to an infinite class of quantum measurements whose operator's Fourier spectrum is concentrated on low degree terms. We
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low-degree learning algorithm which is a quantum counterpart of (Linial et al., 1993)
learning algorithm and show that the quantum sample complexity depends on the ``compatibility structure" of such measurement classes -- the more compatible the class is, the lower the quantum sample complexity will be. We further introduce k-junta measurements as a special class of low-depth quantum circuits whose Fourier spectrum is concentrated on low degrees