We carry out a hybrid Monte Carlo (HMC) simulation of the
$SU(2)/\mathbb{Z}_2$ Yang--Mills theory in which the $\mathbb{Z}_N$ 2-form flat
gauge field (the 't~Hooft flux) is explicitly treated as one of dynamical
variables. We observe that our HMC algorithm in the $SU(2)/\mathbb{Z}_2$ theory
drastically reduces autocorrelation lengths of the topological charge and a
physical quantity which couples to slow modes in the conventional HMC
simulation of the $SU(2)$ theory. Provided that sufficiently large lattice
volumes are available, therefore, the HMC algorithm of the $SU(N)/\mathbb{Z}_N$
theory could be employed as an alternative for the simulation of the $SU(N)$
Yang--Mills theory, because local observables are expected to be insensitive to
the difference between $SU(N)$ and~$SU(N)/\mathbb{Z}_N$ in the large volume
limit. A possible method to incorporate quarks (fermions in the fundamental
representation of~$SU(N)$ with the baryon number~1ドル/N$) in this framework is
also considered.