Dynamical Lie algebras generated by Pauli strings and quadratic spaces over $\mathbb{F}_2$

Hans Cuypers

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arXiv · 2603.08373

Dynamical Lie algebras generated by Pauli strings and quadratic spaces over $\mathbb{F}_2$

Hans Cuypers

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Abstract

Dynamical Lie algebras, i.e. Lie subalgebras of $\mathfrak{su}(2^n)$, generated by Pauli strings have recently been studied intensively. They are also called Pauli Lie algebras or Hamiltonian Lie algebras. In this paper we provide a uniform mathematical approach to various recent results on Pauli Lie algebras. Moreover, we present an algorithm that on input of a set of Pauli strings determines the isomorphism type of the dynamical Lie algebra generated by these Pauli's in time $\mathcal{O}(\max(n,m)^3)$ where $m$ is the size of the generating set.

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BibTeX RIS

Hans Cuypers. 2026-03-09. Dynamical Lie algebras generated by Pauli strings and quadratic spaces over $\mathbb{F}_2$. https://arxiv.org/abs/2603.08373

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