We introduce Weyl Josephson circuits: small Josephson junction circuits that simulate Weyl band structures. We first formulate a general approach to design circuits that are analogous to Bloch Hamiltonians of a desired dimensionality and symmetry class. We then construct and analyze a six-junction device that produces a 3D Weyl Hamiltonian with broken inversion symmetry and in which topological phase transitions can be triggered emph{in situ}. We argue that currently available superconducting circuit technology allows experiments that probe topological properties inaccessible in condensed matter systems.
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