Experimental Preparation of Topologically Ordered States via Adiabatic Evolution

Abstract: Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can arise in two-dimensional spin-lattice models. In this paper, we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution. The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators. Each sector is highly entangled, as shown from the completely reconstructed density matrices. This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.