  Multipartite entanglement of large numbers of physically distinct linear
resonators is of both fundamental and applied interest, but there have been no
feasible proposals to date for achieving it. At the same time, the Bose-Hubbard
model with attractive interactions (ABH) is theoretically known to have a phase
transition from the superfluid phase to a highly entangled nonlocal
superposition, but observation of this phase transition has remained out of
experimental reach. In this theoretical work, we jointly address these two
problems by (1) proposing an experimentally accessible quantum simulation of
the ABH phase transition in an array of tunably coupled superconducting circuit
microwave resonators and (2) incorporating the simulation into a highly
scalable protocol that takes as input any microwave resonator state with
negligible occupation of number states |0> and |1> and nonlocally superposes it
across the whole array of resonators. The large-scale multipartite entanglement
produced by the protocol is of the W-type, which is well-known for its
robustness. The protocol utilizes the ABH phase transition to generate the
multipartite entanglement of all of the resonators in parallel, and is
therefore deterministic and permits an increase in resonator number without
increase in protocol complexity; the number of resonators is limited instead by
system characteristics such as resonator frequency disorder and inter-resonator
coupling strength. Only one local and two global controls are required for the
protocol. We numerically demonstrate the protocol with realistic system
parameters, and estimate that current experimental capabilities can realize the
protocol with high fidelity for greater than 40 resonators.
