Diagrammatic Approach to Quantum Search
Thomas G. Wong

TL;DR
This paper presents a diagrammatic method for analyzing quantum search algorithms on graphs, enabling estimation of search dynamics in complex subspaces using perturbation theory.
Contribution
It introduces a novel diagrammatic approach combined with degenerate perturbation theory to analyze quantum search on large, complex graphs.
Findings
First example of degenerate perturbation theory applied to graph-based quantum search
Method allows estimation of search dynamics in high-dimensional subspaces
Provides a new tool for analyzing quantum walks on complex graphs
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 .
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