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arXiv · 2608.30771

PauLie: Fast Classification of Pauli Dynamical Lie Algebras

Oxana Shaya·Konstantin Golovkin·Mainak Roy·Vincent Russo
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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 $O(n|\mathcal{G}|\max(n,|\mathcal{G}|))$ time, where $|\mathcal{G}|$ 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.

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Oxana Shaya, Konstantin Golovkin, Mainak Roy, Vincent Russo. 2026-08-31. PauLie: Fast Classification of Pauli Dynamical Lie Algebras. https://arxiv.org/abs/2608.30771

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