Fast convergence of propagation algorithms for open quantum systems
Abstract
We establish general conditions for the rapid convergence of propagation algorithms for computing expectation values of local observables in quantum many-body systems, covering both spin and fermionic systems. Our results apply to evolutions that are sufficiently contractive, providing a general mechanism by which contractivity controls the growth generated by local interactions and enables efficient classical simulation. As a first application, we consider noisy time evolution generated by local Hamiltonians on arbitrary interaction graphs. We show that the dynamics can be efficiently simulated when the noise strength λ is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength u, our bounds determine a time horizon tmax as a function of the interaction strength u, the noise strength λ, and the interaction structure below which the algorithm is efficient. In the noiseless limit, λ=0, our analysis extends the efficiently simulable time scale from log(1/u) proved in Facelli, Fawzi, and Fawzi (2026) to tmax ∼ 1/u matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength u, our result applies up to inverse temperatures β∼log(1/u).
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BibTeX
@misc{facelli2026fast,
title = {{Fast convergence of propagation algorithms for open quantum systems}},
author = {Giorgio Facelli and Hamza Fawzi and Omar Fawzi and Cambyse Rouzé and Sam Slezak and Daniel Stilck França},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06769},
eprint = {2610.06769},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06769},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fast convergence of propagation algorithms for open quantum systems
AU - Giorgio Facelli
AU - Hamza Fawzi
AU - Omar Fawzi
AU - Cambyse Rouzé
AU - Sam Slezak
AU - Daniel Stilck França
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06769
UR - https://arxiv.org/abs/2610.06769
AB - We establish general conditions for the rapid convergence of propagation algorithms for computing expectation values of local observables in quantum many-body systems, covering both spin and fermionic systems. Our results apply to evolutions that are sufficiently contractive, providing a general mechanism by which contractivity controls the growth generated by local interactions and enables efficient classical simulation. As a first application, we consider noisy time evolution generated by local Hamiltonians on arbitrary interaction graphs. We show that the dynamics can be efficiently simulated when the noise strength λ is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength u, our bounds determine a time horizon t_max as a function of the interaction strength u, the noise strength λ, and the interaction structure below which the algorithm is efficient. In the noiseless limit, λ=0, our analysis extends the efficiently simulable time scale from log(1/u) proved in Facelli, Fawzi, and Fawzi (2026) to t_max ∼ 1/u matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength u, our result applies up to inverse temperatures β∼log(1/u).
ER -