We present a 3D topological picture-language for quantum information.
Our approach combines charged excitations carried by
strings, with topological properties that arise from embedding the
strings in the interior of a 3D manifold with boundary. A quon is
a composite that acts as a particle. Specifically, a quon is a hemisphere
containing a neutral pair of open strings with opposite
charge. We interpret multiquons and their transformations in a
natural way. We obtain a type of relation, a string–genus “joint
relation,” involving both a string and the 3D manifold. We use
the joint relation to obtain a topological interpretation of the C*
Hopf algebra relations, which are widely used in tensor networks.
We obtain a 3D representation of the controlled NOT (CNOT) gate
that is considerably simpler than earlier work, and a 3D topological
protocol for teleportation.