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arXiv:2610.39350

Provably efficient experimental classification of quantum data with quantum kernels

Keitaro Anai, Akimoto Nakayama, Shintaro Ooka, Hiroko Tomoda, Yuto Morohoshi, Yohji Chin, Shigehito Miki, Masahiro Yabuno, Hirotaka Terai, Peter van Loock, Kosuke Mitarai, Shuntaro Takeda

quant-phSubmitted Oct 29, 2026• Announced Oct 30, 2026• 0 citations
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Abstract

Analyzing quantum systems is essential for quantum information processing, but can require exponentially many measurements without exploiting the structure of the system or task. Quantum machine learning offers a promising way to reduce this cost by learning from quantum data. Here, we theoretically establish a framework for efficient quantum-state classification and experimentally demonstrate the resulting scheme on a programmable photonic processor. Our analysis links learning efficiency to the structure of quantum data, without relying on a physical description tailored to each task. We derive sufficient conditions for accurate classification with a number of measurements polynomial in system size. We apply this guarantee to a resource problem in continuous-variable (CV) quantum computing: classifying stellar rank, a measure of non-Gaussianity. Experimentally, we implement the classification of single-mode CV quantum states with stellar rank zero and one. This is enabled by developing a programmable CV photonic processor capable of preparing and processing diverse Gaussian and non-Gaussian states and performing virtual projection onto such states, going beyond the Gaussian-only capabilities of most existing photonic platforms. The experiment demonstrates accurate classification despite experimental imperfections. Our results establish a theory-guided and experimentally validated framework for quantum-state classification that can be implemented on quantum devices available today.

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9 pages, 5 figures for the main text, and 22 pages and 6 figures for the supplementary information

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Analyzing quantum systems is essential for quantum information processing, but can require exponentially many measurements without exploiting the structure of the system or task. Quantum machine learning offers a promising way to reduce this cost by learning from quantum data. Here, we theoretically establish a framework for efficient quantum-state classification and experimentally demonstrate the resulting scheme on a programmable photonic processor. Our analysis links learning efficiency to the structure of quantum data, without relying on a physical description tailored to each task. We derive sufficient conditions for accurate classification with a number of measurements polynomial in system size. We apply this guarantee to a resource problem in continuous-variable (CV) quantum computing: classifying stellar rank, a measure of non-Gaussianity. Experimentally, we implement the classification of single-mode CV quantum states with stellar rank zero and one. This is enabled by developing a programmable CV photonic processor capable of preparing and processing diverse Gaussian and non-Gaussian states and performing virtual projection onto such states, going beyond the Gaussian-only capabilities of most existing photonic platforms. The experiment demonstrates accurate classification despite experimental imperfections. Our results establish a theory-guided and experimentally validated framework for quantum-state classification that can be implemented on quantum devices available today.
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The past decades have seen the development of quantum machine learning, stemming from the intersection of quantum computing and machine learning. This field is particularly promising for the design of alternative quantum (or quantum inspired) computation paradigms that could require fewer resources with respect to standard ones, e.g., in terms of energy consumption. In this context, we present the implementation of a data reuploading scheme on a photonic integrated processor, achieving high accuracies in several image classification tasks. We thoroughly investigate the capabilities of this apparently simple model, which relies on the evolution of one-qubit states, by providing an analytical proof that our implementation is a universal classifier and an effective learner, capable of generalizing to new, unknown data. Hence, our results not only demonstrate data reuploading in a potentially resource-efficient optical implementation but also provide theoretical insight into this algorithm, its trainability, and generalizability properties. This lays the groundwork for developing more resource-efficient machine learning algorithms, leveraging our scheme as a subroutine.
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We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable (CV) quantum circuits. This family of circuits is suited to describe optical quantum technologies and in particular it includes state-of-the-art photonic processors capable of showing quantum advantage. We define classes of functions that map classical variables, encoded into the CV circuit parameters, to outcome probabilities evaluated on those circuits. We then establish efficient learnability guarantees for such classes, by computing bounds on their pseudo-dimension or covering numbers, showing that CV quantum circuits can be learned with a sample complexity that scales polynomially with the circuit's size, i.e., the number of modes. Our results show that CV circuits can be trained efficiently using a number of training samples that, unlike their finite-dimensional counterpart, does not scale with the circuit depth.