  Gauge theory is the framework of the Standard Model of particle physics and
is also important in condensed matter physics. As its major non-perturbative
approach, lattice gauge theory is traditionally implemented using Monte Carlo
simulation, consequently it usually suffers such problems as the Fermion sign
problem and the lack of real-time dynamics. Hopefully they can be avoided by
using quantum simulation, which simulates quantum systems by using controllable
true quantum processes. The field of quantum simulation is under rapid
development. Here we present a circuit-based digital scheme of quantum
simulation of quantum $\mathbb{Z}_2$ lattice gauge theory in $2+1$ and $3+1$
dimensions, using quantum adiabatic algorithms implemented in terms of
universal quantum gates. Our algorithm generalizes the Trotter and symmetric
decompositions to the case that the Hamiltonian varies at each step in the
decomposition. Furthermore, we carry through a complete demonstration of this
scheme in classical GPU simulator, and obtain key features of quantum
$\mathbb{Z}_2$ lattice gauge theory, including quantum phase transitions,
topological properties, gauge invariance and duality. Hereby dubbed
pseudoquantum simulation, classical demonstration of quantum simulation in
state-of-art fast computers not only facilitates the development of schemes and
algorithms of real quantum simulation, but also represents a new approach of
practical computation.
