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The imminent realization of topologically-protected qubits in fabricatedsystems will provide not only an elementary implementation of fault-tolerantquantum computing architecture, but also an experimental vehicle for thegeneral study of topological order. The simplest topological qubit harbors whatis known as a Z$_2$ liquid phase, which encodes information via a degeneracydepending on the system's topology. Elementary excitations of the phase arefractionally charged objects called {\it spinons}, or Ising flux vorticescalled {\it visons}. At zero temperature a Z$_2$ liquid is stable underdeformations of the Hamiltonian until spinon or vison condensation induces aquantum phase transition destroying the topological order. In this paper, weuse quantum Monte Carlo to study a vison-induced transition from a Z$_2$ liquidto a valence-bond solid in a quantum dimer model on the kagome lattice. Ourresults indicate that this critical point is controlled by a new universalityclass beyond the standard Landau paradigm.

Destroying a topological quantum bit by condensing Ising vortices