  Quantum phenomena have the potential to speed up the solution of hard
optimization problems. For example quantum annealing, based on the quantum
tunneling effect, has recently been shown to scale exponentially better with
system size as compared with classical simulated annealing. However, current
realizations of quantum annealers with superconducting qubits face two major
challenges. First, the connectivity between the qubits is limited, excluding
many optimization problems from a direct implementation. Second, decoherence
degrades the success probability of the optimization. We address both of these
shortcomings and propose an architecture in which the qubits are robustly
encoded in continuous variable degrees of freedom. Remarkably, by leveraging
the phenomenon of flux quantization, all-to-all connectivity is obtained
without overhead. Furthermore, we demonstrate the robustness of this
architecture by simulating the optimal solution of a small instance of the
NP-hard and fully connected number partitioning problem in the presence of
dissipation.
