English

Faster randomized partial trace estimation

Numerical Analysis 2024-12-02 v2 Strongly Correlated Electrons Numerical Analysis Quantum Physics

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.

Keywords

Cite

@article{arxiv.2310.12364,
  title  = {Faster randomized partial trace estimation},
  author = {Tyler Chen and Robert Chen and Kevin Li and Skai Nzeuton and Yilu Pan and Yixin Wang},
  journal= {arXiv preprint arXiv:2310.12364},
  year   = {2024}
}