The TEMPO network can be made independent of the system size
Abstract
The time-evolving matrix product operator (TEMPO) method efficiently simulates non-Markovian open quantum system dynamics by contracting a two-dimensional tensor network representing the time-discretized Feynman-Vernon influence functional. The standard form of this network has an unfavorable scaling with the size of the system. We show that, within the usual second-order time-step error, the dimensions of all internal network bonds can be reduced to (2m+1)(m+1), where m is the number of independent coupling channels. This dimension does not depend on the number of distinct eigenvalues of the coupling operators. The system size only enters in the final boundary layer of the network, making large system sizes accessible to TEMPO methods. This structure was discovered by Claude Opus 5.5 during guided algorithm development.
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BibTeX
@misc{link2026tempo,
title = {{The TEMPO network can be made independent of the system size}},
author = {Valentin Link},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37012},
eprint = {2610.37012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37012},
}
RIS
TY - UNPB
TI - The TEMPO network can be made independent of the system size
AU - Valentin Link
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37012
UR - https://arxiv.org/abs/2610.37012
AB - The time-evolving matrix product operator (TEMPO) method efficiently simulates non-Markovian open quantum system dynamics by contracting a two-dimensional tensor network representing the time-discretized Feynman-Vernon influence functional. The standard form of this network has an unfavorable scaling with the size of the system. We show that, within the usual second-order time-step error, the dimensions of all internal network bonds can be reduced to (2m+1)(m+1), where m is the number of independent coupling channels. This dimension does not depend on the number of distinct eigenvalues of the coupling operators. The system size only enters in the final boundary layer of the network, making large system sizes accessible to TEMPO methods. This structure was discovered by Claude Opus 5.5 during guided algorithm development.
ER -