Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory

Quantum Physics [Submitted on 4 Jun 2026] Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the (1+1)d \mathbb{Z}_2 lattice gauge theory Kanta Yamanaka, Takanori Daiza, Katsumi Imaizumi, Yutaro Iiyama, Lento Nagano, Ryu Sawada, Koji Terashi We perform detailed studies of five Hamiltonian variational ansatzes (HVA) based on the Hamiltonian of the (1+1)d \mathbb{Z}_2 lattice gauge theory. The ansatzes are designed to respect local and global symmetries of the original Hamiltonian and therefore act on a finely segmented state Hilbert space. Following Larocca et al. (2023), we numerically study the dimension of the dynamical Lie algebra (DLA) and the rank of the quantum Fisher information matrix (QFIM) of the ansatzes within specific invariant subspaces. The ansatzes all involve sums of weight-three Paulis in their generators, which is a feature that have so far been underexplored in this context. We also perform numerical experiments to determine the ground state energy of the original Hamiltonian via variational quantum eigensolver (VQE), and observe that overparametrization of the ansatzes coincides with the apparent disappearance of local minima in the loss function, in line with the finding in the reference. Finally, the decay rate of the VQE loss function under gradient descent optimization is revealed to scale linearly with the number of parameters in the ansatz. These results help to enrich the theory of overparameterization of quantum circuits and inform the design of scalable variational ansatzes. Comments: 13 pages, 5 figures Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat) Cite as: arXiv:2606.05719 [quant-ph]   (or arXiv:2606.05719v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05719 Focus to learn more Submission history From: Yutaro Iiyama [view email] [v1] Thu, 4 Jun 2026 05:23:17 UTC (93 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 Change to browse by: hep-lat References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)