Quantum Walks with Gremlin

TL;DR

This paper explores how the Gremlin graph traversal language can be used to analyze and simulate quantum walks on complex graph structures, bridging quantum computing and graph theory.

Contribution

It introduces a novel approach to simulate quantum walks using Gremlin, enabling numerical analysis and conceptual integration of quantum principles into graph traversal.

Findings

Gremlin facilitates numerical simulation of quantum walks on complex graphs.

Quantum walk principles can be integrated into classical graph traversals.

The approach enables cross-disciplinary insights between quantum computing and graph theory.

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.