title: Adiabatic preparation of topological order.
abstract: Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms of local order parameters. Here we show that a system of n spins forming a lattice on a Riemann surface can undergo a second order quantum phase transition between a spin-polarized phase and a string-net condensed phase. This is an example of a quantum phase transition between magnetic and topological order. We furthermore show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by O(sqrt[n]). This provides a physically plausible method for constructing and initializing a topological quantum memory.
authors.affiliation: Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA.
authors.forename: Alioscia
authors.initials: A
authors.lastname: Hamma
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Lidar