Vladimir Kornyak touches on some of these ideas in these papers:<p>1. On Compatibility of Discrete Relations (2005) <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;math-ph&#x2F;0504048.pdf" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;math-ph&#x2F;0504048.pdf</a><p>2. Structural and Symmetry Analysis of Discrete Dynamical Systems (2010) <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1006.1754.pdf" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1006.1754.pdf</a><p>3. Discrete Dynamical Models: Combinatorics,
Statistics and Continuum Approximations (2015) <a href="http:&#x2F;&#x2F;mmg.tversu.ru&#x2F;images&#x2F;publications&#x2F;2015-vol3-n1&#x2F;Kornyak-2015-01-05.pdf" rel="nofollow">http:&#x2F;&#x2F;mmg.tversu.ru&#x2F;images&#x2F;publications&#x2F;2015-vol3-n1&#x2F;Kornya...</a><p>On a somewhat related note -- applying quantum principles to graph database processing -- see this new paper by Marko Rodriguez (the creator of the Gremlin graph programming language):<p>4. Quantum Walks with Gremlin (2015) <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1511.06278v1.pdf" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1511.06278v1.pdf</a>