Quantum Walks with Gremlin

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.