  We study disordered interacting bosons described by the Bose-Hubbard model
with Gaussian-distributed random tunneling amplitudes. It is shown that the
off-diagonal disorder induces a spin-glass-like ground state, characterized by
randomly frozen quantum-mechanical U(1) phases of bosons. To access
criticality, we employ the "$n$-replica trick", as in the spin-glass theory,
and the Trotter-Suzuki method for decomposition of the statistical density
operator, along with numerical calculations. The interplay between disorder,
quantum and thermal fluctuations leads to phase diagrams exhibiting a glassy
state of bosons, which are studied as a function of model parameters. The
considered system may be relevant for quantum simulators of optical-lattice
bosons, where the randomness can be introduced in a controlled way. The latter
is supported by a proposition of experimental realization of the system in
question.
