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.