Learning quantum many-body data locally: A provably scalable framework

2025-09-17

AI Summary

Recent near-term quantum devices suffer from limited data acquisition capabilities, hindering large-scale quantum many-body machine learning. To address this, we propose the provably scalable Geometrically Local Quantum Kernel (GLQK) framework. GLQK is the first kernel design to explicitly incorporate both the exponential decay of quantum correlations and geometric locality—leveraging quantum shadows and local observables to encode the physical system’s local structure directly in feature space. Theoretically, for translationally invariant systems, GLQK achieves constant sample complexity independent of qubit count, yielding an exponential improvement in sample efficiency over existing shadow-based kernels. Numerical experiments demonstrate GLQK’s superior scalability across two canonical tasks: expectation-value estimation and quantum state classification—significantly reducing data requirements on noisy intermediate-scale quantum (NISQ) hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments. This approach can efficiently solve certain quantum problems that are classically intractable, suggesting potential advantages of harnessing quantum data. However, addressing large-scale problems still requires significant amounts of data beyond the limited computational resources of near-term quantum devices. We propose a scalable ML framework called Geometrically Local Quantum Kernel (GLQK), designed to efficiently learn quantum many-body experimental data by leveraging the exponential decay of correlations, a phenomenon prevalent in noncritical systems. In the task of learning an unknown polynomial of quantum expectation values, we rigorously prove that GLQK substantially improves polynomial sample complexity in the number of qubits $n$, compared to 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, GLQK achieves constant sample complexity, independent of $n$. We numerically demonstrate its high scalability in two learning tasks on quantum many-body phenomena. These results establish new avenues for utilizing experimental data to advance the understanding of quantum many-body physics.

Problem

• Efficiently learning quantum many-body data locally
• Reducing sample complexity for quantum expectation polynomials
• Achieving scalable machine learning for quantum experiments

Innovation

• Geometrically Local Quantum Kernel framework
• Leverages exponential decay of correlations
• Local quantum information feature space