On Information Propagation in Krylov Subspaces
Abstract
Krylov subspace methods provide an efficient tool for modeling any quantum initial value problem as a one dimensional chain. A time ordered path formulation, in which the dynamical generator successively splits probability between paths, yields a speed limit within such dynamical subspaces. For power law growing Lanczos coefficients bn ∼ nδ we find super ballistic lightcones, with an exponentially spreading lightcone for maximal growth δ= 1. Causality in the Krylov chain constrains the Lanczos coefficients to grow at most linearly. We illustrate the validity of the above in the $SL(2, R)$ and Heisenberg Weyl algebras, and in a many body skew field Ising model. Moreover, we extend the above bound to the family of Q complexities. Lastly, mapping to a spin chain gives a Lieb Robinson bound analogue and opens the problem to standard condensed matter methods.
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BibTeX
@misc{martinezazcona2026information,
title = {{On Information Propagation in Krylov Subspaces}},
author = {Pablo Martinez-Azcona and Maximilian Meyer-Moelleringhof and Adolfo del Campo and Apollonas S. Matsoukas-Roubeas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03883},
eprint = {2610.03883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03883},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Information Propagation in Krylov Subspaces
AU - Pablo Martinez-Azcona
AU - Maximilian Meyer-Moelleringhof
AU - Adolfo del Campo
AU - Apollonas S. Matsoukas-Roubeas
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03883
UR - https://arxiv.org/abs/2610.03883
AB - Krylov subspace methods provide an efficient tool for modeling any quantum initial value problem as a one dimensional chain. A time ordered path formulation, in which the dynamical generator successively splits probability between paths, yields a speed limit within such dynamical subspaces. For power law growing Lanczos coefficients b_n ∼ n^δ we find super ballistic lightcones, with an exponentially spreading lightcone for maximal growth δ= 1. Causality in the Krylov chain constrains the Lanczos coefficients to grow at most linearly. We illustrate the validity of the above in the $SL(2, R)$ and Heisenberg Weyl algebras, and in a many body skew field Ising model. Moreover, we extend the above bound to the family of Q complexities. Lastly, mapping to a spin chain gives a Lieb Robinson bound analogue and opens the problem to standard condensed matter methods.
ER -