PauLie: Fast Classification of Pauli Dynamical Lie Algebras
Abstract
The dynamical Lie algebra (DLA) governs the controllability, expressibility, and simulation complexity of a quantum system. Explicitly computing it has been a major computational bottleneck: brute-force Lie closure scales exponentially in the number of qubits n. Many applications, however, consult only the isomorphism type of the DLA. We introduce PauLie, an open-source framework that decides this isomorphism type for DLAs generated by arbitrary Pauli strings, building on the anticommutation-graph reduction of Aguilar et al. PauLie runs in O(n|𝒢|max(n,|𝒢|)) time, where |𝒢| is the number of generators, turning DLA classification into a routine preprocessing step. We demonstrate its use as a structural oracle for routing Lie-algebraic simulation and Cartan decomposition, diagnosing barren plateaus in variational quantum algorithms, and engineering universal Pauli string generator sets with optimal generation rate.
Related
- Pauli propagation enables fast classical simulation of strongly correlated quantum systems
- Anticommuting Displacement Operators, Exact Pauli Algebras,and the Singlet State from the Oscillator Vacuum
- Dynamical Lie Algebras for Fixed-Gate Quantum Ansätze
- Subspace Controllability in Variational Quantum Circuits: Maximising Expressivity and Increasing Search Efficiency with Dynamical Lie Algebras
- Fast dynamical control of quantum droplets via Feshbach resonances
BibTeX
@misc{shaya2026paulie,
title = {{PauLie: Fast Classification of Pauli Dynamical Lie Algebras}},
author = {Oxana Shaya and Konstantin Golovkin and Mainak Roy and Vincent Russo},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30771},
eprint = {2608.30771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30771},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - PauLie: Fast Classification of Pauli Dynamical Lie Algebras
AU - Oxana Shaya
AU - Konstantin Golovkin
AU - Mainak Roy
AU - Vincent Russo
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30771
UR - https://arxiv.org/abs/2608.30771
AB - The dynamical Lie algebra (DLA) governs the controllability, expressibility, and simulation complexity of a quantum system. Explicitly computing it has been a major computational bottleneck: brute-force Lie closure scales exponentially in the number of qubits n. Many applications, however, consult only the isomorphism type of the DLA. We introduce PauLie, an open-source framework that decides this isomorphism type for DLAs generated by arbitrary Pauli strings, building on the anticommutation-graph reduction of Aguilar et al. PauLie runs in O(n|𝒢|max(n,|𝒢|)) time, where |𝒢| is the number of generators, turning DLA classification into a routine preprocessing step. We demonstrate its use as a structural oracle for routing Lie-algebraic simulation and Cartan decomposition, diagnosing barren plateaus in variational quantum algorithms, and engineering universal Pauli string generator sets with optimal generation rate.
ER -