Quantum Computing Seminar

Speaker: Jason Suagee (GWU)
Place: Monroe 115
Date and Time: Thursday, December 4, 11:10-12:25pm
Title: The Adiabatic Theorem in Quantum Mechanics and Geometric Phase

Abstract: After briefly discussing the general solution to the time independent Shrodinger wave equation, I will introduce the Adiabatic Theorem which is an underlying phenomenon in quantum mechanics involved in topological quantum computing. The Adiabatic theorem states that if we alter a Hamiltonian gradually from some initial form H^i to a final form
H^f then a particle initially in the n-th eigenstate of H^I will be carried to the n-th eigenstate of H^f. I will then introduce the idea of geometric phase, and derive an explicit way to calculate it supposing that the conditions of the Adiabatic Theorem are valid. I will end by discussing the relationship between abelian anyons, braiding anyons through time, and the geometric phase.