Quantum Walks with Gremlin [Graph Day, Austin]

Quantum Walks with Gremlin by Marko A. Rodiguez, Jennifer H. Watkins.

Abstract:

A quantum walk places a traverser into a superposition of both graph location and traversal “spin.” The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the sampling of the probability distribution generated from the quantum wavefunction. Simple quantum walks are studied analytically, but for large graph structures with complex topologies, numerical solutions are typically required. For the quantum theorist, the Gremlin graph traversal machine and language can be used for the numerical analysis of quantum walks on such structures. Additionally, for the graph theorist, the adoption of quantum walk principles can transform what are currently side-effect laden traversals into pure, stateless functional flows. This is true even when the constraints of quantum mechanics are not fully respected (e.g. reversible and unitary evolution). In sum, Gremlin allows both types of theorist to leverage each other’s constructs for the advancement of their respective disciplines.

Best not to tackle this new paper on Gremlin and quantum graph walks after a heavy meal. 😉

Marko will be presenting at Graph Day, 17 January 2016, Austin, Texas. Great opportunity to hear him speak along with other cutting edge graph folks.

The walk Marko describes is located in a Hilbert space. Understandable because numerical solutions require the use of a metric space.

However, if you are modeling semantics in difference universes of discourse, realize that semantics don’t possess metric spaces. Semantics lie outside of metric space, although I concede that many have imposed varying arbitrary metrics on semantics.

For example, if I am mapping the English term for “black,” as in a color to the term “schwartz” in German, I need a “traverser” that enables the existence of both terms at separate locations, one for each universe in the graph.

You may protest that is overly complex for the representation of synonyms, but consider that “schwartz” occupies a different location in the universe of German and etymology from “black.”

For advertising, subtleties of language may not be useful, but for reading medical or technical works, an “approximate” or “almost right” meaning may be more damaging than helpful.

Who knows? Perhaps quantum computers will come closer to modeling semantics across domains better than any computer to date. Not perfectly but closer.

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