# Achievement

## Using quantum random walks to study the graph isomorphism problem

### Project

IGERT: Geometry and Dynamics -- Integrated Education in the Mathematical Sciences

### University

Brandeis University

(Waltham, MA)

### PI

## Trainee Achievements

### Using quantum random walks to study the graph isomorphism problem

Blake Stacey, in a rotation with Albion Lawrence, made interesting progress on using quantum random walks to study the graph isomorphism problem, following on work by Susan Coppersmith at UW-Madison. This uses a physics approach to a problem in computer science; Stacey learned a lot about (and taught Lawrence about) both sides of he problem, obtaining interesting preliminary numerical results by studying the the wavefunction of quantum random walkers in graphs with various connectivity properties. Stacey also developed an algorithm using classical random walks to detect community structures in graphs, which has potential use in mathematical models of population dynamics.

- “Trainee Achievements”
- Achievements for this Project