  We study an experimentally feasible system of strongly correlated bosons with
random hoppings, described by the infinite-range Bose-Hubbard model on a
lattice with hopping integrals given by independent random variables of
Gaussian distribution with non-zero mean. We solve this quantum model in the
thermodynamic limit, employing the replica method and the Trotter-Suzuki
formula. We find and describe a superglass phase that emerges at the interface
between glass and superfluid phases. Both glassy and long-range orderings are
present in the superglass and compete with each other, as revealed by the
anticorrelation of their order parameters. We present phase diagrams in various
cross-sections of the multidimensional space of system parameters. In selected
parameter subspaces, we compare the results to those of non-disordered,
diagonally-disordered, and once celebrated spin-glass systems.
