Topology Statistics And Universal Quantum Computation In Ultra-Cold Atomic Cases

Topology, Statistics, and Universal Quantum Computation in Ultra-cold Atomic Gases

Changwei Zhang

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. I will discuss two topological states of matter in ultra-cold atomic gases: chiral p-wave superfluids of fermionic cold atoms and Kitaev model for bosonic atoms in optical lattices. I will show how to create and braid topological quantum excitations in these two systems and how to observe their braiding statistics. Observation of the braiding statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. I will show how to test the quantum non-locality of the topological excitations and how to implement universal quantum computation in chiral p-wave superfluids.