Louis Kauffman

This talk will prove that there is a universal set of gates for quantum computing consisting in A single unitary solution R to the Yang-Baxter equation. Local unitary single qubit operations. The matrix R is the change of basis matrix taking the standard basis of a 2-qubit vector space to the Bell basis. This matrix is not only a unitary solution to the Yang-Baxter equation, it also gives rise to an interesting invariant of knots and links. This talk will pivot on this Theorem and discuss relationships between braids, knots, topological and quantum entanglement and quantum computing. From the point of view of this Theorem, any quantum computer can be configured as representation of an element in a generalization of the Artin Braid group. (This is joint work with Sam Lomonaco.)