Quantum Computation and Information Seminar 

08/05/2009, 15:00 — 16:00 — Room P4.35, Mathematics Building
Victor Atanasov, SQIG-IT

Geometry in Quantum Mechanics: Qubits from Knots

A quantum particle conned within a nanotube (light in an optical waveg- uide) feels the bending of the axis of that tube via the geometry-induced po- tential. As a result the quantum dynamics is coupled with the solutions of the equations for the shape of this nanotube. We will elaborate on the emergence and properties of this geometry-induced potential due to connement. An interesting application represents the open tight trefoil knot which cur- vature prole induces a quantum two-well potential for an electron trapped in its interior, namely the trefoil knot can act as a qubit. A collection of knots on a quantum wire may be used for quantum computation. The same is valid for the closed trefoil knot which also represents a quantum simulation of one dimensional solid.