Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2509.13705

Provably scalable learning from quantum many-body data via locality

Koki Chinzei, Quoc Hoan Tran, Norifumi Matsumoto, Yasuhiro Endo, Hirotaka Oshima

Published Sep 17, 2025• 0 citations
arXivHTMLPDF

Abstract

Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments, potentially solving certain classically intractable problems. However, addressing large-scale problems still requires significant amounts of data that exceed the capabilities of near-term quantum devices. We propose a scalable ML framework, the Geometrically Local Quantum Kernel (GLQK), that efficiently learns from quantum many-body data by leveraging the exponential decay of correlations prevalent in noncritical systems. For learning an unknown polynomial of quantum expectation values, we rigorously prove that the GLQK substantially improves the sample complexity in the system size $n$ over the existing shadow kernel, by constructing a feature space from local quantum information at the correlation length scale. This improvement is particularly notable when each term of the target polynomial involves few local subsystems. Remarkably, for translationally symmetric data, the GLQK achieves constant sample complexity, independent of $n$. Numerical experiments on two quantum many-body tasks corroborate these theoretical results, demonstrating the high scalability of the GLQK. Beyond the polynomial setting, we further show that it can efficiently learn certain non-polynomial functions. Our framework establishes new avenues for utilizing experimental data to advance the understanding of quantum many-body physics.

DOI
10.48550/arxiv.2509.13705

Related papers

Exponentially improved efficient machine learning for quantum many-body states with provable guarantees

Yanming Che, Clemens Gneiting, Franco Nori

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m -dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ , provided that a sample set (of size N ) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N = m O ( 1 ɛ ) , was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n , with N = poly ( ɛ − 1 , n , ln 1 δ ) , where poly denotes a polynomial function, and ( 1 − δ ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N = poly ( ɛ − 1 , ln n δ ) . Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024

arXiv:2304.04353•Physical Review Research•Jul 8, 2024•8 citations

Large-scale quantum reservoir learning with an analog quantum computer

Milan Kornjača, Hong-Ye Hu, Chen Zhao +50 more

Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks.

arXiv:2407.02553•Jul 2, 2024•9 citations

Learning quantum many-body systems from a few copies

Cambyse Rouzé, Daniel Stilck França

Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all quasi-local observables of a state from a number of copies that scales polylogarithmically with the system's size and polynomially on the locality of the target observables. We show that this constitutes a provable exponential improvement in the number of copies over state-of-the-art tomography protocols. We achieve our results by combining the maximum entropy method with tools from the emerging fields of classical shadows and quantum optimal transport. The latter allows us to fine-tune the error made in estimating the expectation value of an observable in terms of how local it is and how well we approximate the expectation value of a fixed set of few-body observables. We conjecture that our condition holds for all states exhibiting some form of decay of correlations and establish it for several subsets thereof. These include widely studied classes of states such as one-dimensional thermal and high-temperature Gibbs states of local commuting Hamiltonians on arbitrary hypergraphs or outputs of shallow circuits. Moreover, we show improvements of the maximum entropy method beyond the sample complexity that are of independent interest. These include identifying regimes in which it is possible to perform the postprocessing efficiently as well as novel bounds on the condition number of covariance matrices of many-body states.

arXiv:2107.03333•Quantum•Apr 30, 2024•26 citations

A Hybrid Quantum Machine Learning Framework Based on Nyström Approximation for Scalability Enhancement of Quantum Kernels

Mohammad Hossein Rezvannia

Abstract Quantum Machine Learning (QML) is an emerging field at the intersection of quantum computing and artificial intelligence, offering high potential for extracting complex nonlinear patterns from high-dimensional data. However, many quantum kernel-based methods suffer from high computational costs, the requirement for numerous quantum circuit executions, and the limitations of current Noisy Intermediate-Scale Quantum (NISQ) hardware. These challenges, particularly when dealing with large datasets, represent a major barrier to the widespread adoption of these methods in practical applications. In this paper, a hybrid quantum machine learning framework based on Nyström approximation is proposed to effectively reduce the computational complexity of quantum kernels and enhance their scalability. In the proposed framework, classical data is first mapped to the quantum Hilbert space via parameterized quantum circuits, and the quantum kernel is defined based on the overlap of quantum states. Then, utilizing the Nyström approximation technique, the full kernel calculation is restricted to a representative subset of data, and the final learning process is conducted in the classical space. This approach reduces computational complexity from \(\:O\left({N}^{2}\right)\) to \(\:O\left(Nm\right)\), where N is the number of samples and m is the size of the selected subset. Analytical results and simulations on the Breast Cancer Wisconsin dataset demonstrate that the proposed framework reduces computational costs by over 60% while maintaining the geometric structure of the quantum feature space, with a classification accuracy loss of less than 3%. These results suggest that the proposed method can serve as a practical, scalable, and noise-resilient solution for applying quantum machine learning to real-world data-driven problems.

•Feb 18, 2026•0 citations

Quantum machine learning beyond kernel methods

Sofiène Jerbi, Lukas J. Fiderer, Hendrik Poulsen Nautrup +3 more

Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and studied extensively. Yet, our understanding of how these models compare, both mutually and to classical models, remains limited. In this work, we identify a constructive framework that captures all standard models based on parametrized quantum circuits: that of linear quantum models. In particular, we show using tools from quantum information theory how data re-uploading circuits, an apparent outlier of this framework, can be efficiently mapped into the simpler picture of linear models in quantum Hilbert spaces. Furthermore, we analyze the experimentally-relevant resource requirements of these models in terms of qubit number and amount of data needed to learn. Based on recent results from classical machine learning, we prove that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points. Our results provide a more comprehensive view of quantum machine learning models as well as insights on the compatibility of different models with NISQ constraints.

arXiv:2110.13162•Nature Communications•Jan 31, 2023•238 citations

Provable learning separation for predicting time-evolution of quantum many-body systems

Rahul Bandyopadhyay, Riccardo Molteni, Jens Eisert +2 more

Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations? We address this problem by studying the learnability of quantum many-body dynamics from the perspective of probably approximately correct (PAC)-learning. Concretely, we devise a supervised learning problem where the training set consists of specifications of randomized stabilizer probe states, evolution times sampled uniformly from a polynomially large time interval $[0,T]$, coupled with expectation values of certain observables evaluated on the resulting time-evolved state under an unknown Hamiltonian. For this learning task, we provide an efficient quantum procedure whose training phase learns the underlying Hamiltonian from short-time training samples, and whose deployment phase combines Hamiltonian simulation with the classical shadows protocol to perform inference on a newly given data point. By contrast, the existence of $O(\mathsf{poly}(n))$-time instances ensures classical hardness: by embedding a $\mathsf{BQP}$-complete computation into the polynomially long time-dynamics of a low-intersection variant of the Feynman-Kitaev clock Hamiltonian construction, we show that, for a certain family of input distributions, no randomized classical polynomial-time algorithm can fulfill our learning condition, unless $\mathsf{BQP}\subseteq\mathsf{P/poly}$. Furthermore, we show that the classically hard instance maintains quantum learnability. We also give an interpretation of our results in learning-assisted certified quantum simulation. Taken together, our results demonstrate a rigorous learning separation for a natural ML task based on Hamiltonian evolution, while building connections between quantum learning theory, quantum simulation, and QML.

quant-pharXiv:2607.06472•Jul 8, 2026•0 citations
Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments, potentially solving certain classically intractable problems. However, addressing large-scale problems still requires significant amounts of data that exceed the capabilities of near-term quantum devices. We propose a scalable ML framework, the Geometrically Local Quantum Kernel (GLQK), that efficiently learns from quantum many-body data by leveraging the exponential decay of correlations prevalent in noncritical systems. For learning an unknown polynomial of quantum expectation values, we rigorously prove that the GLQK substantially improves the sample complexity in the system size nnn over the existing shadow kernel, by constructing a feature space from local quantum information at the correlation length scale. This improvement is particularly notable when each term of the target polynomial involves few local subsystems. Remarkably, for translationally symmetric data, the GLQK achieves constant sample complexity, independent of nnn. Numerical experiments on two quantum many-body tasks corroborate these theoretical results, demonstrating the high scalability of the GLQK. Beyond the polynomial setting, we further show that it can efficiently learn certain non-polynomial functions. Our framework establishes new avenues for utilizing experimental data to advance the understanding of quantum many-body physics.
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m -dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ , provided that a sample set (of size N ) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N = m O ( 1 ɛ ) , was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n , with N = poly ( ɛ − 1 , n , ln 1 δ ) , where poly denotes a polynomial function, and ( 1 − δ ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N = poly ( ɛ − 1 , ln n δ ) . Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024
Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks.
Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all quasi-local observables of a state from a number of copies that scales polylogarithmically with the system's size and polynomially on the locality of the target observables. We show that this constitutes a provable exponential improvement in the number of copies over state-of-the-art tomography protocols. We achieve our results by combining the maximum entropy method with tools from the emerging fields of classical shadows and quantum optimal transport. The latter allows us to fine-tune the error made in estimating the expectation value of an observable in terms of how local it is and how well we approximate the expectation value of a fixed set of few-body observables. We conjecture that our condition holds for all states exhibiting some form of decay of correlations and establish it for several subsets thereof. These include widely studied classes of states such as one-dimensional thermal and high-temperature Gibbs states of local commuting Hamiltonians on arbitrary hypergraphs or outputs of shallow circuits. Moreover, we show improvements of the maximum entropy method beyond the sample complexity that are of independent interest. These include identifying regimes in which it is possible to perform the postprocessing efficiently as well as novel bounds on the condition number of covariance matrices of many-body states.
Abstract Quantum Machine Learning (QML) is an emerging field at the intersection of quantum computing and artificial intelligence, offering high potential for extracting complex nonlinear patterns from high-dimensional data. However, many quantum kernel-based methods suffer from high computational costs, the requirement for numerous quantum circuit executions, and the limitations of current Noisy Intermediate-Scale Quantum (NISQ) hardware. These challenges, particularly when dealing with large datasets, represent a major barrier to the widespread adoption of these methods in practical applications. In this paper, a hybrid quantum machine learning framework based on Nyström approximation is proposed to effectively reduce the computational complexity of quantum kernels and enhance their scalability. In the proposed framework, classical data is first mapped to the quantum Hilbert space via parameterized quantum circuits, and the quantum kernel is defined based on the overlap of quantum states. Then, utilizing the Nyström approximation technique, the full kernel calculation is restricted to a representative subset of data, and the final learning process is conducted in the classical space. This approach reduces computational complexity from  O(N2)\:O\left({N}^{2}\right)O(N2) to  O(Nm)\:O\left(Nm\right)O(Nm), where N is the number of samples and m is the size of the selected subset. Analytical results and simulations on the Breast Cancer Wisconsin dataset demonstrate that the proposed framework reduces computational costs by over 60% while maintaining the geometric structure of the quantum feature space, with a classification accuracy loss of less than 3%. These results suggest that the proposed method can serve as a practical, scalable, and noise-resilient solution for applying quantum machine learning to real-world data-driven problems.
Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and studied extensively. Yet, our understanding of how these models compare, both mutually and to classical models, remains limited. In this work, we identify a constructive framework that captures all standard models based on parametrized quantum circuits: that of linear quantum models. In particular, we show using tools from quantum information theory how data re-uploading circuits, an apparent outlier of this framework, can be efficiently mapped into the simpler picture of linear models in quantum Hilbert spaces. Furthermore, we analyze the experimentally-relevant resource requirements of these models in terms of qubit number and amount of data needed to learn. Based on recent results from classical machine learning, we prove that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points. Our results provide a more comprehensive view of quantum machine learning models as well as insights on the compatibility of different models with NISQ constraints.
Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations? We address this problem by studying the learnability of quantum many-body dynamics from the perspective of probably approximately correct (PAC)-learning. Concretely, we devise a supervised learning problem where the training set consists of specifications of randomized stabilizer probe states, evolution times sampled uniformly from a polynomially large time interval [0,T][0,T][0,T], coupled with expectation values of certain observables evaluated on the resulting time-evolved state under an unknown Hamiltonian. For this learning task, we provide an efficient quantum procedure whose training phase learns the underlying Hamiltonian from short-time training samples, and whose deployment phase combines Hamiltonian simulation with the classical shadows protocol to perform inference on a newly given data point. By contrast, the existence of O(poly(n))O(\mathsf{poly}(n))O(poly(n))-time instances ensures classical hardness: by embedding a BQP\mathsf{BQP}BQP-complete computation into the polynomially long time-dynamics of a low-intersection variant of the Feynman-Kitaev clock Hamiltonian construction, we show that, for a certain family of input distributions, no randomized classical polynomial-time algorithm can fulfill our learning condition, unless BQP⊆P/poly\mathsf{BQP}\subseteq\mathsf{P/poly}BQP⊆P/poly. Furthermore, we show that the classically hard instance maintains quantum learnability. We also give an interpretation of our results in learning-assisted certified quantum simulation. Taken together, our results demonstrate a rigorous learning separation for a natural ML task based on Hamiltonian evolution, while building connections between quantum learning theory, quantum simulation, and QML.