Efficient Hamiltonian, structure and trace distance learning of Gaussian states.
6 affiliations
- 1Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris, Palaiseau, France. [email protected].
- 2Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark. [email protected].
- 3Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain. [email protected].
- 4Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris, Palaiseau, France.
- 5Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
- 6Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, Lyon, France.
Abstract
When learning descriptions of many-body quantum systems, assuming locality of interactions can dramatically reduce the required number of observations and computational time compared to unstructured approaches. In this work, we uncover an infinite-dimensional instance of this phenomenon, initiating the study of Hamiltonian learning for positive-temperature bosonic Gaussian states. We present sample- and computationally efficient protocols for inferring the parameters and graph structure of underlying quadratic Hamiltonians, provided that temperature, squeezing, displacement, and the interaction graph's maximal degree are bounded. Notably, our protocol relies solely on heterodyne measurements, which are often experimentally feasible, and achieves a sample complexity that scales only logarithmically with the number of modes. Furthermore, our techniques allow for the learning of positive-temperature Gaussian states in trace distance with quadratic scaling in precision and polynomial scaling in the number of modes.
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BibTeX
@article{fanizza2026efficient,
title = {{Efficient Hamiltonian, structure and trace distance learning of Gaussian states.}},
author = {Marco Fanizza and Cambyse Rouzé and Daniel Stilck França},
journal = {Nature communications},
year = {2026},
month = sep,
doi = {10.1038/s41467-026-77405-3},
url = {https://europepmc.org/article/MED/42893996},
note = {CC BY},
}
RIS
TY - JOUR
TI - Efficient Hamiltonian, structure and trace distance learning of Gaussian states.
AU - Marco Fanizza
AU - Cambyse Rouzé
AU - Daniel Stilck França
PY - 2026
DA - 2026/09/16
JO - Nature communications
DO - 10.1038/s41467-026-77405-3
UR - https://europepmc.org/article/MED/42893996
AB - When learning descriptions of many-body quantum systems, assuming locality of interactions can dramatically reduce the required number of observations and computational time compared to unstructured approaches. In this work, we uncover an infinite-dimensional instance of this phenomenon, initiating the study of Hamiltonian learning for positive-temperature bosonic Gaussian states. We present sample- and computationally efficient protocols for inferring the parameters and graph structure of underlying quadratic Hamiltonians, provided that temperature, squeezing, displacement, and the interaction graph's maximal degree are bounded. Notably, our protocol relies solely on heterodyne measurements, which are often experimentally feasible, and achieves a sample complexity that scales only logarithmically with the number of modes. Furthermore, our techniques allow for the learning of positive-temperature Gaussian states in trace distance with quadratic scaling in precision and polynomial scaling in the number of modes.
SN - 2041-1723
ER -