PreprintCC BY 4.0arXiv
Improved convergence radius of the Fer expansion for Hermitian generators
Abstract
The Dyson series expands the propagator of a time-dependent Hamiltonian in powers of the Hamiltonian, but its truncations are in general not unitary. The Fer expansion writes the same propagator as an infinite product of matrix exponentials, each of them unitary, and its remainder decays doubly exponentially with the number of factors. Convergence, however, is guaranteed only within a finite radius: the time integral of the norm of the Hamiltonian must be smaller than $2$. This is the best value known to date. Here we improve it by about 30%, raising it to about $2.6058$. The result also holds for non-Hermitian Hamiltonians that are Hermitian with respect to a fixed metric.
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BibTeX
@misc{bagnasacco2026improved,
title = {{Improved convergence radius of the Fer expansion for Hermitian generators}},
author = {Lorenzo Bagnasacco and Vittorio Giovannetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28302},
eprint = {2609.28302},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28302},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved convergence radius of the Fer expansion for Hermitian generators
AU - Lorenzo Bagnasacco
AU - Vittorio Giovannetti
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.28302
UR - https://arxiv.org/abs/2609.28302
AB - The Dyson series expands the propagator of a time-dependent Hamiltonian in powers of the Hamiltonian, but its truncations are in general not unitary. The Fer expansion writes the same propagator as an infinite product of matrix exponentials, each of them unitary, and its remainder decays doubly exponentially with the number of factors. Convergence, however, is guaranteed only within a finite radius: the time integral of the norm of the Hamiltonian must be smaller than $2$. This is the best value known to date. Here we improve it by about 30%, raising it to about $2.6058$. The result also holds for non-Hermitian Hamiltonians that are Hermitian with respect to a fixed metric.
ER -