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arXiv · 2310.12364

Faster randomized partial trace estimation

Tyler Chen·Robert Chen·Kevin Li·Skai Nzeuton·Yilu Pan·Yixin Wang
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Abstract

We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng, \emph{Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems}, J. Chem. Phys. 157, 064106 (2022)] by deflating important subspaces (e.g. corresponding to the low-energy eigenstates) explicitly. This results in a significant variance reduction, leading to several order-of-magnitude speedups over the previous state of the art. We then apply our algorithm to study the thermodynamics of several Heisenberg spin systems, particularly the entanglement spectrum and ergotropy.

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Tyler Chen, Robert Chen, Kevin Li, Skai Nzeuton, Yilu Pan, Yixin Wang. 2023-10-18. Faster randomized partial trace estimation. https://doi.org/10.1137/23m1620399

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