FASTER RANDOMIZED PARTIAL TRACE ESTIMATION

Tyler Chen

doi:10.1137/23M1620399

FASTER RANDOMIZED PARTIAL TRACE ESTIMATION

2024-11-04

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DOI：10.1137/23M1620399

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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, J. Chem. Phys., 157 (2022), 064106] 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 the study of the thermodynamics of several Heisenberg spin systems, particularly the entanglement spectrum and ergotropy.

Keywords:

partial trace

deflation

stochastic trace

Krylov subspace method

FASTER RANDOMIZED PARTIAL TRACE ESTIMATION

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