  We propose to construct large quantum graph codes by means of superconducting
circuits working at the ultrastrong coupling regime. In this physical scenario,
we are able to create a cluster state between any pair of qubits within a
fraction of a nanosecond. To exemplify our proposal, creation of the five-qubit
and Steane codes is numerically simulated. We also provide optimal operating
conditions with which the graph codes can be realized with state-of-the-art
superconducting technologies.
