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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Theoretical Computer Science
- Electronic, Optical and Magnetic Materials
- Signal Processing
- Modeling and Simulation
- Electrical and Electronic Engineering