Complexity of quantum states in the stabilizer formalism
Quantum Physics
2026-04-23 v1
Abstract
We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of quantum computation. This is achieved by leveraging the symmetric Jordan product (associated with classicality) and the skew-symmetric Lie product (linked to quantumness) between the square root of the quantum state and the Heisenberg-Weyl displacement operators. We establish the fundamental properties of this quantifier and demonstrate that state complexity is closely related to the nonstabilizerness of quantum states via the -norm of their characteristic functions.
Keywords
Cite
@article{arxiv.2604.20118,
title = {Complexity of quantum states in the stabilizer formalism},
author = {Shuangshuang Fu and Shunlong Luo and Yue Zhang},
journal= {arXiv preprint arXiv:2604.20118},
year = {2026}
}