PreprintarXiv licencearXiv
Dynamical Lie Algebras for Fixed-Gate Quantum Ansätze
Abstract
Parameterized Quantum Circuits have emerged as a central framework for variational quantum algorithms in the NISQ regime, with major applications in quantum simulation, combinatorial optimization, and, more recently, quantum machine learning (QML). By developing a new approach for computing dynamical Lie algebras associated with quantum circuits combining parametrized gates and non-parametrized entangling gates, we aim to extend the applicability of recent algebraic results to architectures that are actually used in quantum machine learning.
Related
- Rotation fixed points of undecorated braid varieties and fusion rings of affine Lie algebras
- Finite BM-algebras and fixed-point combinators
- Universality from Quadratic Angular-Momentum Operations: Exact Dynamical Lie Algebras and the Role of the Casimir Obstruction
- Wave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry
- Dynamical C*-algebras and coarse geometry
BibTeX
@misc{zang2026dynamical,
title = {{Dynamical Lie Algebras for Fixed-Gate Quantum Ansätze}},
author = {Orlane Zang and Daniel Juteau and Tony Quertier and Grégoire Barrué},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13709},
eprint = {2610.13709},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13709},
}
RIS
TY - UNPB
TI - Dynamical Lie Algebras for Fixed-Gate Quantum Ansätze
AU - Orlane Zang
AU - Daniel Juteau
AU - Tony Quertier
AU - Grégoire Barrué
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.13709
UR - https://arxiv.org/abs/2610.13709
AB - Parameterized Quantum Circuits have emerged as a central framework for variational quantum algorithms in the NISQ regime, with major applications in quantum simulation, combinatorial optimization, and, more recently, quantum machine learning (QML). By developing a new approach for computing dynamical Lie algebras associated with quantum circuits combining parametrized gates and non-parametrized entangling gates, we aim to extend the applicability of recent algebraic results to architectures that are actually used in quantum machine learning.
ER -