  Extending the methods from our previous work on quantum knots and quantum
graphs, we describe a general procedure for quantizing a large class of
mathematical structures which includes, for example, knots, graphs, groups,
algebraic varieties, categories, topological spaces, geometric spaces, and
more. This procedure is different from that normally found in quantum topology.
  We then demonstrate the power of this method by using it to quantize braids.
This general method produces a blueprint of a quantum system which is
physically implementable in the same sense that Shor's quantum factoring
algorithm is physically implementable. Mathematical invariants become objects
that are physically observable.
