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. We show that the classical results carry over to the quantum case when fluctuations are gradually tuned via the wire capacitances, yielding Z_2 quantum topological order. In an extreme quantum limit where the capacitances are all small, we arrive at an effective quantum spin Hamiltonian that we conjecture would sustain Z_2 quantum topological order with a gap of the order of the Josephson coupling in the array.