Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper ‘Quantum knots and mosaics’ arxiv 
to give a precise and workable definition of quantum knots, intended to represent an actual physical quantum system.
~
LOMONACO JR, Samuel J. and KAUFFMAN, Louis H., 2008. Quantum Knots and Mosaics. arXiv:0805.0339 [quant-ph]. Online. 3 May 2008. [Accessed 30 April 2022]. Available from: http://arxiv.org/abs/0805.0339
> In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. > > This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the “quantum embodiment” of a closed knotted physical piece of rope. A quantum knot, as a state of this system, represents the state of such a knotted closed piece of rope, i.e., the particular spatial configuration of the knot tied in the rope. Associated with a quantum knot system is a group of unitary transformations, called the ambient group, which represents all possible ways of moving the rope around (without cutting the rope, and without letting the rope pass through itself.) Of course, unlike a classical closed piece of rope, a quantum knot can exhibit non-classical behavior, such as quantum superposition and quantum entanglement. This raises some interesting and puzzling questions about the relation between topological and quantum entanglement. The knot type of a quantum knot is simply the orbit of the quantum knot under the action of the ambient group. We investigate quantum observables which are invariants of quantum knot type. We also study the Hamiltonians associated with the generators of the ambient group, and briefly look at the quantum tunneling of overcrossings into undercrossings. A basic building block in this paper is a mosaic system which is a formal (rewriting) system of symbol strings. We conjecture that this formal system fully captures in an axiomatic way all of the properties of tame knot theory.arXiv: 0805.0339
DOT strict digraph rankdir=LR node [style=filled fillcolor=lightyellow penwidth=3 color=black fontname="Helvetica"] HERE NODE node [style=filled fillcolor=lightblue] WHERE /^Next/ LINKS HERE -> NODE node [style=filled fillcolor=white] HERE NODE WHERE /^Next/ LINKS HERE -> NODE node [style=filled fillcolor=white penwidth=3 color=black] LINKS HERE -> NODE node [style=filled fillcolor=white penwidth=1 color=black] HERE NODE LINKS HERE -> NODE node [style="filled,rounded,dotted" fillcolor=white] edge [style=dotted] HERE NODE BACKLINKS NODE -> HERE