aiqbench analysis
This research establishes rigorous convergence guarantees for truncated hierarchical equations of motion (HEOM) in finite-dimensional open quantum systems, ensuring numerical stability without spurious modes as truncation depth increases. By proving spectral consistency using Schur-complement terminators, the study provides a robust mathematical foundation for simulating complex quantum dynamics like those in the spin-boson model with high fidelity.
On truncations of hierarchical equations of motion for finite-dimensional systems
arXiv:2604.22568v2 Announce Type: replace Abstract: We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges to that of the full HEOM as the truncation depth increases. We also prove that this approximation is free of spectral pollution: sufficiently deep truncations do not produce spurious unstable modes, provided the exact HEOM is stable. We illustrate the results for the spin-boson model.
Abstract:We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges to that of the full HEOM as the truncation depth increases. We also prove that this approximation is free of spectral pollution: sufficiently deep truncations do not produce spurious unstable modes, provided the exact HEOM is stable. We illustrate the results for the spin-boson model.
arXiv:2604.22568 [quant-ph]
(or arXiv:2604.22568v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2604.22568 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 164 words
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