Lecture 21. Anyons

0:00 Various physical implementations of qubits 1:51 Bosons and fermions 7:33 Bohm-Aharonov effect 11:45 Anyons 21:56 Quasiparticles 23:59 Toric model 32:09 Energy spectrum in the toric model 46:18 Excitations in the toric model 54:32 Topological aspects in the toric model: moving charges in a closed loop Anyons are quasiparticles that form a foundation of topological quantum computing. The main property of the anyons is that their wave function acquires a phase shift when two anyons are moved around each other. With this property anyons (any-ons) generalize the notions of bosons (whose wave function is symmetric) and fermions (whose wave function switches sign when two fermions are interchanged). Anyons may be realized as quasiparticles in 2-dimensional electron fluids. To illustrate the notion of quasiparticles and to exhibit their topological properties we discuss Kitaev's toric model. This is a lecture in a graduate course "Quantum Computing". My book "Quantum Computing for High School Students" is available here: https://qubitpublishing.com/ or from Amazon. Complete playlist for this course: https://www.youtube.com/playlist?list=PLu6jbin1VpDD87rdSDF4HRfITWF_LwgOx