  We propose a superconducting quantum circuit based on a general symmetry
principle -- combinatorial gauge symmetry -- designed to emulate
topologically-ordered quantum liquids and serve as a foundation for the
construction of topological qubits. The proposed circuit exhibits rich
features: in the classical limit of large capacitances its ground state
consists of two superimposed loop structures; one is a crystal of small loops
containing disordered $U(1)$ degrees of freedom, and the other is a gas of
loops of all sizes associated to $\mathbb{Z}_2$ topological order. We show that
these classical results carry over to the quantum case, where phase
fluctuations arise from the presence of finite capacitances, yielding ${\mathbb
Z}_2$ quantum topological order. A key feature of the exact gauge symmetry is
that amplitudes connecting different ${\mathbb Z}_2$ loop states arise from
paths having zero classical energy cost. As a result, these amplitudes are
controlled by dimensional confinement rather than tunneling through energy
barriers. We argue that this effect may lead to larger energy gaps than
previous proposals which are limited by such barriers, potentially making it
more likely for a topological phase to be experimentally observable. Finally,
we discuss how our superconducting circuit realization of combinatorial gauge
symmetry can be implemented in practice.
