  Quantum computation represents an emerging framework to solve lattice gauge
theories (LGT) with arbitrary gauge groups, a general and long-standing problem
in computational physics. While quantum computers may encode LGT using only
polynomially increasing resources, a major openissue concerns the violation of
gauge-invariance during the dynamics and the search for groundstates. Here, we
propose a new class of parametrized quantum circuits that can represent states
belonging only to the physical sector of the total Hilbert space. This class of
circuits is compact yet flexible enough to be used as a variational ansatz to
study ground state properties, as well as representing states originating from
a real-time dynamics. Concerning the first application, the structure of the
wavefunction ansatz guarantees the preservation of physical constraints such as
the Gauss law along the entire optimization process, enabling reliable
variational calculations. As for the second application, this class of quantum
circuits can be used in combination with timedependent variational quantum
algorithms, thus drastically reducing the resource requirements to access
dynamical properties.
