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DOE OSTI · 3365177

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Erpenbeck, André [Univ. of Michigan, Ann Arbor, MI (United States); Univ. of Georgia, Athens, GA (United States)] (ORCID:0000000249078074)·Zhu, Yuanran [Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Applied Mathematics and Computational Research Division]·Yu, Yang [Univ. of Michigan, Ann Arbor, MI (United States)] (ORCID:0000000186178878)·Zhang, Lei [Univ. of Michigan, Ann Arbor, MI (United States)] (ORCID:0000000288284639)·Gerum, Richard [York Univ., Toronto, ON (Canada)] (ORCID:0000000158932650)·Goulko, Olga [University of Massachusetts, Boston, MA (United States)] (ORCID:0000000318950904)·Yang, Chao [Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Applied Mathematics and Computational Research Division]·Cohen, Guy [Tel Aviv Univ., Tel Aviv (Israel)] (ORCID:0000000174044055)·Gull, Emanuel [Univ. of Michigan, Ann Arbor, MI (United States); Univ. of Warsaw (Poland)] (ORCID:0000000260821260)
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Abstract

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and we show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.

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BibTeXRIS

Erpenbeck, André [Univ. of Michigan, Ann Arbor, MI (United States); Univ. of Georgia, Athens, GA (United States)] (ORCID:0000000249078074), Zhu, Yuanran [Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Applied Mathematics and Computational Research Division], Yu, Yang [Univ. of Michigan, Ann Arbor, MI (United States)] (ORCID:0000000186178878), Zhang, Lei [Univ. of Michigan, Ann Arbor, MI (United States)] (ORCID:0000000288284639), Gerum, Richard [York Univ., Toronto, ON (Canada)] (ORCID:0000000158932650), Goulko, Olga [University of Massachusetts, Boston, MA (United States)] (ORCID:0000000318950904), Yang, Chao [Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Applied Mathematics and Computational Research Division], Cohen, Guy [Tel Aviv Univ., Tel Aviv (Israel)] (ORCID:0000000174044055), Gull, Emanuel [Univ. of Michigan, Ann Arbor, MI (United States); Univ. of Warsaw (Poland)] (ORCID:0000000260821260). 2026-03-16. Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm. https://doi.org/10.1103/8vzv-y74m

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