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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.
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extre
It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum Computation.
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of topological order with the spontaneous breaking of discrete time-translation symmetry. We show that many-body localiz
Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum simulation o
Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many scenarios, the p