  We study some properties of generalized global symmetry for the charge-$q$
Schwinger model in the Hamiltonian formalism, which is the $(1+1)$-dimensional
quantum electrodynamics with a charge-$q$ Dirac fermion. This model has the
$\mathbb{Z}_q$ $1$-form symmetry, which is a remnant of the electric $U(1)$
$1$-form symmetry in the pure Maxwell theory. It is known that if we put the
theory on closed space, then the Hilbert space is decomposed into $q$ distinct
sectors, called universes and some states with higher energy density do not
decay to the ground state due to the selection rule of the $1$-form symmetry.
Even with open boundaries, we can observe the stability of such states by
seeing a negative string tension behavior, meaning that opposite charges repel
with each other. We develop a method based on the adiabatic state preparation
to see this feature with digital quantum simulation and confirm it using a
classical simulator of quantum devices. Especially, we measure local energy
density and see how it jumps between inside and outside of insertion of the
probe charges. We explicitly see that the energy density inside is lower than
the outside one. This is a clear signature of the negative string tension.
