Maximum-Entropy Extension of Quantum Correlation Functions from Short Real-Time Dynamics
Abstract
Correlation functions are central to understanding the behavior of quantum systems, with their spectra giving direct access to quasiparticle and collective excitations. However, the long-time evolution required for sufficient spectral resolution is challenging to reach for both classical and quantum simulations. In this work, we introduce a principled approach for extending time series of quantum correlation functions and reconstructing their spectral densities, based on their connection with covariance sequences of stationary stochastic processes. This connection enables us to apply Burg's maximum-entropy principle to find the least-committal extension compatible with the measured values of the correlation function, which corresponds to an all-pole autoregressive model whose coefficients solve a set of Yule--Walker equations. The resulting extension is positive semi-definite by construction, guaranteeing the positivity of the spectrum and the automatic satisfaction of its total spectral weight sum rule. The approach applies to both scalar and matrix-valued correlation functions, including those with highly structured or continuous spectra. The generalization to the matrix case makes it possible to trade simulation time for additional measured correlation functions, enabling accurate time-series extension and spectral reconstruction from short-time data, even in the presence of noise.
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BibTeX
@misc{gambetta2026maximumentropy,
title = {{Maximum-Entropy Extension of Quantum Correlation Functions from Short Real-Time Dynamics}},
author = {Filippo Maria Gambetta and Sabrina Yue Wang and Raul A. Santos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03696},
eprint = {2610.03696},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03696},
}
RIS
TY - UNPB
TI - Maximum-Entropy Extension of Quantum Correlation Functions from Short Real-Time Dynamics
AU - Filippo Maria Gambetta
AU - Sabrina Yue Wang
AU - Raul A. Santos
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03696
UR - https://arxiv.org/abs/2610.03696
AB - Correlation functions are central to understanding the behavior of quantum systems, with their spectra giving direct access to quasiparticle and collective excitations. However, the long-time evolution required for sufficient spectral resolution is challenging to reach for both classical and quantum simulations. In this work, we introduce a principled approach for extending time series of quantum correlation functions and reconstructing their spectral densities, based on their connection with covariance sequences of stationary stochastic processes. This connection enables us to apply Burg's maximum-entropy principle to find the least-committal extension compatible with the measured values of the correlation function, which corresponds to an all-pole autoregressive model whose coefficients solve a set of Yule--Walker equations. The resulting extension is positive semi-definite by construction, guaranteeing the positivity of the spectrum and the automatic satisfaction of its total spectral weight sum rule. The approach applies to both scalar and matrix-valued correlation functions, including those with highly structured or continuous spectra. The generalization to the matrix case makes it possible to trade simulation time for additional measured correlation functions, enabling accurate time-series extension and spectral reconstruction from short-time data, even in the presence of noise.
ER -