Deterministic many-resonator W-entanglement of nearly arbitrary microwave states via attractive Bose-Hubbard simulation

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.