**Upcoming talks**

July 26th

Speaker: Thomas Wong

Affiliation: Creighton University

Title: Equivalent Laplacian and Adjacency Quantum Walks on Irregular Graphs

Abstract: The continuous-time quantum walk is a particle evolving by Schrödinger’s equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems, however, the Hamiltonian is proportional to the adjacency matrix instead. It is well-known that these quantum walks are equivalent when the graph is regular, i.e., when each vertex has the same number of neighbors. If the graph is irregular, however, the quantum walks evolve differently. In this paper, we show that for some irregular graphs, if the particle is initially localized at a certain vertex, the probability distributions of the two quantum walks are identical, even though the amplitudes differ. We analytically prove this for a graph with five vertices and a graph with six vertices. By simulating the walks on all 1,018,689,568 simple, connected, irregular graphs with eleven vertices or less, we found sixty-four graphs with this notion of equivalence. We also give eight infinite families of graphs supporting these equivalent walks. This is joint work with Joshua Lockhart, and a preprint is available at https://arxiv.org/abs/2107.05580

*August 2nd*

Harmonny Zhan

*August 9th*

Judi McDonald

**Past talks**

Youtube playlist with all talks

48. Mike Tait – Two conjectures on the spread of graphs

47. Gabor Lippner – Asymptotic quantum state transfer using two loops with large weights

46. Lord Kavi – The k-Independence Number