This paper formulates a generalization of our work on quantum knots to explain how to make quantum versions of algebraic and combinatorial structures. We include a description of work of the first author on the construction of Hilbert spaces from the states of the bracket polynomial with applications to algorithms for the Jones polynomial and relations with Khovanov homology. The purpose of this paper is to place such constructions in a general context of the quantization of combinatorial structures.

Date Published: 3 June 2011
PDF: 15 pages
Proc. SPIE 8057, Quantum Information and Computation IX, 80570T (3 June 2011); doi: 10.1117/12.882567

Published in SPIE Proceedings Vol. 8057:
Quantum Information and Computation IX
Eric Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)