Quantizing braids and other mathematical structures: the general quantization procedure

Samuel J. Lomonaco; Louis H. Kauffman

doi:10.1117/12.883681

3 June 2011 Quantizing braids and other mathematical structures: the general quantization procedure

Proceedings Volume 8057, Quantum Information and Computation IX; 805702 (2011) https://doi.org/10.1117/12.883681
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

Abstract

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.

Citation Download Citation

Samuel J. Lomonaco and Louis H. Kauffman "Quantizing braids and other mathematical structures: the general quantization procedure", Proc. SPIE 8057, Quantum Information and Computation IX, 805702 (3 June 2011); https://doi.org/10.1117/12.883681

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