A superconducting circuit realization of combinatorial gauge symmetry
We propose an integrated superconducting circuit design in combination with a general symmetry principle – combinatorial gauge symmetry – to build artificial quantum spin liquids that serve as foundation for the construction of topological qubits. The superconducting wire arrays exhibit rich features. In the classical limit of large capacitances its ground state consists of two superimposed spin liquids; one is a crystal of small loops containing disordered U(1) degrees of freedom, and the other is a soup of loops of all sizes associated to Z_2 topological order.