  In this paper we will present some ideas to use 3D topology for quantum
computing extending ideas from a previous paper. Topological quantum computing
used \textquotedblleft knotted\textquotedblright{} quantum states of
topological phases of matter, called anyons. But anyons are connected with
surface topology. But surfaces have (usually) abelian fundamental groups and
therefore one needs non-abelian anyons to use it for quantum computing. But
usual materials are 3D objects which can admit more complicated topologies.
Here, complements of knots do play a prominent role and are in principle the
main parts to understand 3-manifold topology. For that purpose, we will
construct a quantum system on the complements of a knot in the 3-sphere (see
arXiv:2102.04452 for previous work). The whole system is designed as knotted
superconductor where every crossing is a Josephson junction and the qubit is
realized as flux qubit. We discuss the properties of this systems in particular
the fluxion quantization by using the A-polynomial of the knot. Furthermore we
showed that 2-qubit operations can be realized by linked (knotted)
superconductors again coupled via a Josephson junction.

Quantum Physics;Applied Physics