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arXiv:2403.19947 · Physical Review Research

Forecasting long-time dynamics in quantum many-body systems by dynamic mode decomposition

Ryui Kaneko, Masatoshi Imada, Yoshiyuki Kabashima, Tomi Ohtsuki

Published Jan 23, 2025• 14 citations
arXivHTMLPDF

Abstract

Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a method that utilizes reliable short-time data of physical quantities to accurately forecast long-time behavior of the strongly entangled systems. We straightforwardly employ the simple dynamic mode decomposition (DMD), which is commonly used in fluid dynamics. Despite the simplicity of the method, the effectiveness and applicability of the DMD in quantum many-body systems such as the Ising model in the transverse field at the critical point are demonstrated, even when the time evolution at long time exhibits complicated features such as a volume-law entanglement entropy and consequential power-law decays of correlations characteristic of systems with long-ranged quantum entanglements unlike fluid dynamics. The present method, though simple, enables accurate forecasts amazingly at time as long as nearly an order of magnitude longer than that of the short-time training data. Effects of noise on the accuracy of the forecast are also investigated, because they are important especially when dealing with the experimental data. We find that a few percentages of noise do not affect the prediction accuracy destructively.

DOI
10.1103/physrevresearch.7.013085

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We propose a hybrid approach to simulate quantum many-body dynamics by combining Trotter-based quantum evolution with classical dynamic mode decomposition. In quantum simulation, the interest often lies in estimating observables rather than explicitly obtaining the wave function. Instead of characterizing a quantum state, our method predicts observables of the quantum state at later times by using data from a set of short-time measurements from a quantum computer. For a fixed set of measurements, the global error bound for our method scales at most as O(t3/2)\mathcal{O}(t^{3/2})O(t3/2), with constants determined by the DMD approximation error and the conditioning of the learned modes. We apply our method to quench dynamics in the Hubbard model and nearest neighbor spin systems and show that the observable properties can be predicted up to a reasonable error by controlling the number of data points obtained from the quantum measurements.
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