We perform a digital pseudoquantum simulation of $mathbb{Z}_2$ gauge Higgs model on a $3times 3$ lattice. First we propose the quantum algorithm for the digital quantum simulation, based on Trotter decomposition, quantum adiabatic algorithm and its circuit realization. Then we classically demonstrate it in a GPU simulator, obtaining useful results, which indicate the topological properties of deconfined phase and clarify the phase diagram. Especially, our work suggests that the tricitical point, where the two critical lines of second-order transitions meet, lies on the critical line of the first-order transition rather than its end.
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