Physics-informed quantum algorithms for glueball-like excitations in a $\mathbb{Z}_2$ lattice gauge theory
Glueball spectroscopy and real-time production with quantum computing require three distinct ingredients: a correlated gauge vacuum, a controlled construction of pure-gauge excitations, and a dynamical detector. We develop a physics-informed quantum-algorithm toolbox for these tasks in a $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory. We use the term \emph{glueball-like} for localized closed-flux excitations on the confining side of this Abelian model, without identifying them with the non-Abelian glueballs of QCD. A loop-gas circuit and Hamiltonian variational ansatz prepare the gauge vacuum, Wilson-loop quantum subspace expansion constructs and characterizes low-lying excitations, and eigenvector continuation imports parameter-dependent dressing without a rapidly enlarged explicit loop basis. A Bethe--Salpeter-type transition amplitude quantifies the spatial broadening of the lightest state. For dynamics, a vacuum-dressed contractible-loop counter measures excess production of localized glueball-like structures. Although demonstrated in an Abelian model, the toolbox separates preparation, construction, compression, characterization, and dynamical detection in a form that is naturally extensible to non-Abelian lattice gauge theories.