  We study the quantum ground state phases of the one-dimensional disordered
Bose--Hubbard model with attractive interactions, realized by a chain of
superconducting transmon qubits or cold atoms. We map the phase diagram using
perturbation theory and exact diagonalization. Compared to the repulsive
Bose--Hubbard model, the quantum ground state behavior is dramatically
different. At strong disorder of the on-site energies, all the bosons localize
into the vicinity of a single site, contrary to the Bose glass behavior of the
repulsive model. At weak disorder, depending on hopping, the ground state is
either superfluid or a W state, which is a multi-site and multi-particle
entangled superposition of states where all the bosons occupy a single site. We
show that the robustness of the W phase against disorder diminishes as the
total number of bosons increases.
