Computer Science Department , MS Thesis Presentation , Amulya Mohan " Discrete Quantum Walks with Marked Vertices and Their Average Vertex Mixing Matrices"

Tuesday, April 28, 2026
2:00 p.m. to 3:00 p.m.

Amulya Mohan

MS/PhD student

WPI – Computer Science Department

Tuesday, April 28th, 2026 

Time: 2:00 PM to 3:00 PM

Location: Fuller Labs 141

 

Advisor: Hanmeng Zhan

Reader: Bahman Moraffah

Abstract: 

We study the discrete quantum walk on regular graphs that assigns negative identity coins to marked vertices and Grover coins to unmarked ones. We find combinatorial bases for the eigenspaces of the transtion matrix, and derive a formula for the average vertex mixing matrix M̂. 

We then find bounds for entries in M̂, and study when these bounds are tight. 

In particular, the average probabilities between marked vertices are lower and upper bounded by matrices determined by the induced subgraph A(X)[S], the vertex-deleted subgraph A(X)[S], and the edge deleted subgraph A(X-E(X)). These bounds are tight when the neighborhoods of marked

vertices satisfy the walk-equitability condition.