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 multisite and multiparticle 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.

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• Localization
• Phase diagrams
• Quantum simulation
• Disordered systems
• Superconducting qubits
• Bose-Hubbard model
• Exact diagonalization
• Perturbation theory