Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution

Fuente: arXiv
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Auteurs principaux: Tran, Quoc Hoan, Chinzei, Koki, Endo, Yasuhiro, Oshima, Hirotaka
Format: Preprint
Publié: 2026
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author Tran, Quoc Hoan
Chinzei, Koki
Endo, Yasuhiro
Oshima, Hirotaka
author_facet Tran, Quoc Hoan
Chinzei, Koki
Endo, Yasuhiro
Oshima, Hirotaka
contents Generating quantum data by learning the underlying quantum distribution poses challenges in both theoretical and practical scenarios, yet it is a critical task for understanding quantum systems. A fundamental question in quantum machine learning (QML) is the universality of approximation: whether a parameterized QML model can approximate any quantum distribution. We address this question by proving a universality theorem for the Many-body Projected Ensemble (MPE) framework, a method for quantum state design that uses a single many-body wave function to prepare random states. This demonstrates that MPE can approximate any distribution of pure states within a 1-Wasserstein distance error. This theorem provides a rigorous guarantee of universal expressivity, addressing key theoretical gaps in QML. For practicality, we propose an Incremental MPE variant with layer-wise training to improve the trainability. Numerical experiments on clustered quantum states and quantum chemistry datasets validate MPE's efficacy in learning complex quantum data distributions.
format Preprint
id arxiv_https___arxiv_org_abs_2601_18637
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution
Tran, Quoc Hoan
Chinzei, Koki
Endo, Yasuhiro
Oshima, Hirotaka
Quantum Physics
Machine Learning
Generating quantum data by learning the underlying quantum distribution poses challenges in both theoretical and practical scenarios, yet it is a critical task for understanding quantum systems. A fundamental question in quantum machine learning (QML) is the universality of approximation: whether a parameterized QML model can approximate any quantum distribution. We address this question by proving a universality theorem for the Many-body Projected Ensemble (MPE) framework, a method for quantum state design that uses a single many-body wave function to prepare random states. This demonstrates that MPE can approximate any distribution of pure states within a 1-Wasserstein distance error. This theorem provides a rigorous guarantee of universal expressivity, addressing key theoretical gaps in QML. For practicality, we propose an Incremental MPE variant with layer-wise training to improve the trainability. Numerical experiments on clustered quantum states and quantum chemistry datasets validate MPE's efficacy in learning complex quantum data distributions.
title Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution
topic Quantum Physics
Machine Learning
url https://arxiv.org/abs/2601.18637