  Superconducting microwave circuits with Josephson junctions are a major
platform for quantum computing. To unleash their full capabilities, the
cooperative operation of multiple microwave superconducting circuits is
required. Therefore, designing an efficient protocol to distribute microwave
entanglement remotely becomes a crucial open problem. Here, we propose a
continuous-variable entanglement-swap approach based on optical-microwave
entanglement generation, which can boost the ultimate rate by two orders of
magnitude at state-of-the-art parameter region, compared with traditional
approaches. We further empower the protocol with a hybrid variational
entanglement distillation component to provide huge advantage in the
infidelity-versus-success-probability trade-off. Our protocol can be realized
with near-term device performance, and is robust against non-perfections such
as optical loss and noise. Therefore, our work provides a practical method to
realize efficient quantum links for superconducting microwave quantum
computers.
