<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:math> Quantum Double in a Superconducting Wire Array

We show that a Z3 quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the interwire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry—a local Z3 symmetry involving permutations and shifts by ±2π/3 of the superconducting phases. The sign of the star potential resulting from the...