  We study the three-dimensional random Z(2) lattice gauge theory with Higgs
field, which has the link Higgs coupling $c_1 SUS$ and the plaquette gauge
coupling $c_2 UUUU$. The randomness is introduced by replacing $c_1 \to -c_1$
for each link with the probability $p_1$ and $c_2 \to -c_2$ for each plaquette
with the probability $p_2$. We calculate the phase diagram by a new kind of
mean field theory that does not assume the replica symmetry and also by Monte
Carlo simulations. For the case $p_1=p_2(\equiv p)$, the Monte Carlo
simulations exhibit that (i) the region of the Higgs phase in the Coulomb-Higgs
transition diminishes as $p$ increases, and (ii) the first-order phase
transition between the Higgs and the confinement phases disappear for $p \ge
p_c \simeq 0.01$. We discuss the implications of the results to the quantum
memory studied by Kitaev et al. and the Z(2) gauge neural network on a lattice.
