  We present a quantum algorithm for digital quantum simulation of the
$\mathbb{Z}_2$ gauge-Higgs model on a $3\times 3$ lattice, which is based on
Trotter decomposition, the quantum adiabatic algorithm and its circuit
realization. Then we perform a classical demonstration, dubbed a pseudoquantum
simulation, on a GPU simulator. We obtain useful results on this model, which
suggest the topological properties of the deconfined phase and help to clarify
the phase diagram. It is suggested that the tricitical point, where the
second-order critical lines of deconfinement-confinement transition and of
deconfinement-Higgs transition meet, seems to be on the the first-order
critical line of confinement-Higgs transition, at a point other than the end of
this critical line.

High Energy Physics - Lattice;Other Condensed Matter;Quantum Physics