Interpretable Quantum Photonic Generative Models
Abstract
We propose a physical generative model for learning correlated multivariate data based on homodyne detection of photonic continuous-variable (CV) circuits. We use an N-mode photonic circuit in which two-mode squeezing provides correlations, local phase shifts tune the strength and sign of these correlations, and an adjustable interferometer redistributes them across modes. We train the circuit by matching its Pearson correlation matrix to the one obtained from data. We apply affine post-processing to adjust the marginals independently while keeping the relations intact. We test the model on the multivariate distribution of standardized log returns of financial assets, showing that the photonic model can represent rich correlation structures. We reproduce empirical correlations with residuals below 10−4 for five variables and recover the correct correlation signs for 94% ± 1% of 190 correlation pairs at twenty variables, with 86% of the residuals below $0.1$. As a separate technical contribution, we develop an approach for simulating Kerr gates with small nonlinearity via a Hubbard-Stratonovich expansion, making them suitable for CV-based simulators. Our results establish CV photonic circuits as a platform for interpretable generative learning, suitable for representing and fast sampling of distributions across different application domains.
Related
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- Photonic Chips for Universal Quantum Computing: Retrospective and Prospective
BibTeX
@misc{le2026interpretable,
title = {{Interpretable Quantum Photonic Generative Models}},
author = {Dat Chi Le and Oleksandr Kyriienko},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05354},
eprint = {2611.05354},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05354},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interpretable Quantum Photonic Generative Models
AU - Dat Chi Le
AU - Oleksandr Kyriienko
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05354
UR - https://arxiv.org/abs/2611.05354
AB - We propose a physical generative model for learning correlated multivariate data based on homodyne detection of photonic continuous-variable (CV) circuits. We use an N-mode photonic circuit in which two-mode squeezing provides correlations, local phase shifts tune the strength and sign of these correlations, and an adjustable interferometer redistributes them across modes. We train the circuit by matching its Pearson correlation matrix to the one obtained from data. We apply affine post-processing to adjust the marginals independently while keeping the relations intact. We test the model on the multivariate distribution of standardized log returns of financial assets, showing that the photonic model can represent rich correlation structures. We reproduce empirical correlations with residuals below 10^−4 for five variables and recover the correct correlation signs for 94% ± 1% of 190 correlation pairs at twenty variables, with 86% of the residuals below $0.1$. As a separate technical contribution, we develop an approach for simulating Kerr gates with small nonlinearity via a Hubbard-Stratonovich expansion, making them suitable for CV-based simulators. Our results establish CV photonic circuits as a platform for interpretable generative learning, suitable for representing and fast sampling of distributions across different application domains.
ER -