Topological Orders with Spins and Fermions: Quantum Phases and Computation

Description

This thesis deals with topological orders from two different perspectives: from a condensed matter point of view, where topological orders are considered as breakthrough phases of matter; and from the emerging realm of quantum computation, where topological quantum codes are considered the most appealing platform against decoherence. The thesis reports remarkable studies from both sides. It thoroughly investigates a topological order called the double semion model, a counterpart of the Kitaev model but exhibiting richer quasiparticles as excitations. A new model for symmetry enriched topological order is constructed, which adds an onsite global symmetry to the double semion model. Using this topological phase, a new example of topological code is developed, the semion code, which is non-CSS, additive, non-Pauli and within the stabiliser formalism. Furthermore, the thesis analyses the Rashba spin-orbit coupling within topological insulators, turning the helical edge states into generic edges modes with potential application in spinstronics. New types of topological superconductors are proposed and the novel properties of the correspondingly created Majorana fermions are investigated. These Majorana fermions have inherent properties enabling braiding and the performance of logical gates as fundamental blocks for a universsal quantum computator. Front Matter ....Pages i-xvii Front Matter ....Pages 1-1 Topology in Condensed Matter (Laura Ortiz Martín)....Pages 3-10 Topology in Quantum Information (Laura Ortiz Martín)....Pages 11-15 Front Matter ....Pages 17-17 The Bilayer Double Semion Model (Laura Ortiz Martín)....Pages 19-48 Double Semion Model as a Quantum Memory (Laura Ortiz Martín)....Pages 49-68 Front Matter ....Pages 69-69 Topological Insulators (Laura Ortiz Martín)....Pages 71-92 Topological Superconductors (Laura Ortiz Martín)....Pages 93-118 Front Matter ....Pages 119-119 Summary of Results (Laura Ortiz Martín)....Pages 121-123 Outlook (Laura Ortiz Martín)....Pages 125-127 Back Matter ....Pages 129-168