Diagrammatic Approach to Quantum Search

Abstract

We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate perturbation theory's effects on them. Using this method, we give the first example of degenerate perturbation theory solving search on a graph whose evolution occurs in a subspace whose dimension grows with $N$.

9 pages, 7 figures

References in corpus (2)

• Spatial search by quantum walk
• Connectivity is a Poor Indicator of Fast Quantum Search