2011/05/02 by Samuel J. Lomonaco, Louis H. Kauffman
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structure #Algebraic structures and combinatorial models #Algorithm #Artificial intelligence #Braid #Class (philosophy) #Computer science #Factoring #Mathematics #Observable #Pure mathematics #Quantization (signal processing) #Quantum #Quantum algorithm #Quantum mechanics #Topological Materials and Phenomena #Topology (electrical circuits) #msc:20C35 #msc:57M25 #msc:57M27 #msc:81P15 #msc:81P68 #quant-ph
paper · pdf · doi:10.1117/12.883681
arxiv created 2011/05/02 · openalex publication_date 2011/05/13 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.