Hello, At the beginning of summer I started studying quantum mechanics in my spare time. I realized that many of the concepts in quantum mechanics are similar to "Gremlin mechanics." In particular, both systems exploit particle/traverser superposition. However, what Gremlin doesn't have is an explicit notion of wave dynamics -- a fundamental component of quantum systems. That is, the traversers in Gremlin only constructively interfere (called "bulking"), they never destructively interfere. Upon further exploration, I realized that there are very few articles that discuss the use of waves in graph/network theory. Thus, either there is a rich vein of untapped ideas or the endeavor is a dead end with little to be leveraged. I leaned towards the prior assumption given that discrete quantum mechanics is conveniently modeled as a wave on a graph. This wave is known as the famous "wavefunction" of quantum mechanics' wave-particle duality thesis.
In order to learn, I teach. Thus, for GraphDay in January, I decided to present a talk called "Quantum Processes in Graphs." [http://graphday.com/sessions/#rodriguez] However, to ensure that my knowledge is sound, I thought it prudent to first write an article on the topic. This article is entitled "Quantum Walks with Gremlin" and you can find it referenced in the tweet below. https://twitter.com/twarko/status/667784364210569216 Interestingly, there is little difference between classical wave mechanics and quantum mechanics. I suppose the difference can be naively stated as: "quantum mechanics ultimately 'does something' with the wave." In particular, the quantum wavefunction "collapses" to form a particle upon observation/measurement (in the lexicon of the Copenhagen interpretation). While in classical wave mechanics, the wave itself is the ultimate object of concern. Hopefully, the aforementioned article (and future presentation in January) will allow us to kill two birds with one stone -- we learn how to model waves in graphs and, as a nice amendment, we will also learn about quantum computing. We gain all of this from the familiar perspective of the Gremlin graph traversal machine and language. Enjoy, Marko. http://markorodriguez.com
