Normalizing Flow-Based Bayesian Parameter Estimation for Noisy Quantum States
Abstract
To extract complete information about experimental noisy quantum states, as well as correlations among different physical parameters, we develop an efficient machine learning-assisted framework with the normalizing flow based Bayesian parameter estimation (BPE). By embedding a physically interpretable parameter vector, s, into the quantum state ansatzes, ρ(s), the corresponding parameter distribution p(s|D) is induced from BPE, based on the available experimental data D. The BPE allows us to perform parameter correlation analyses, providing powerful insights about how experimental parameters and related noise sources affect quantum features of the system. As an example, the flexibility of our framework is demonstrated using two different physical ansatzes on the optical cat state experiments, where a noisy single-photon state is added to impure squeezed state. With correlations among the Wigner function negativity, photon-addition fraction, noisy fraction, and pump powers, our framework gives interpretations for complicated experimental mechanisms in generating noisy non-Gaussian states. By leveraging normalizing flow-based neural networks and Bayesian uncertainty estimation, along with physical and experimental constraints incorporated naturally, the valuable information inferred in the posterior learning provides guidelines for experimentalists, as well as theorists, in identifying promising parameters to enhance desirable features.
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BibTeX
@misc{hsieh2026normalizing,
title = {{Normalizing Flow-Based Bayesian Parameter Estimation for Noisy Quantum States}},
author = {Hsien-Yi Hsieh and Yuan-Ting Liu and Juan Camilo Rodrıguez and Yang-Yi Lee and Po-Hang Wang and Ole Steuernagel and Chien-Ming Wu and Ray-Kuang Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19534},
eprint = {2609.19534},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19534},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Normalizing Flow-Based Bayesian Parameter Estimation for Noisy Quantum States
AU - Hsien-Yi Hsieh
AU - Yuan-Ting Liu
AU - Juan Camilo Rodrıguez
AU - Yang-Yi Lee
AU - Po-Hang Wang
AU - Ole Steuernagel
AU - Chien-Ming Wu
AU - Ray-Kuang Lee
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19534
UR - https://arxiv.org/abs/2609.19534
AB - To extract complete information about experimental noisy quantum states, as well as correlations among different physical parameters, we develop an efficient machine learning-assisted framework with the normalizing flow based Bayesian parameter estimation (BPE). By embedding a physically interpretable parameter vector, s, into the quantum state ansatzes, ρ(s), the corresponding parameter distribution p(s|D) is induced from BPE, based on the available experimental data D. The BPE allows us to perform parameter correlation analyses, providing powerful insights about how experimental parameters and related noise sources affect quantum features of the system. As an example, the flexibility of our framework is demonstrated using two different physical ansatzes on the optical cat state experiments, where a noisy single-photon state is added to impure squeezed state. With correlations among the Wigner function negativity, photon-addition fraction, noisy fraction, and pump powers, our framework gives interpretations for complicated experimental mechanisms in generating noisy non-Gaussian states. By leveraging normalizing flow-based neural networks and Bayesian uncertainty estimation, along with physical and experimental constraints incorporated naturally, the valuable information inferred in the posterior learning provides guidelines for experimentalists, as well as theorists, in identifying promising parameters to enhance desirable features.
ER -