33 citations · 67 across the 19 of their papers we have counts for
19 papers
Subdivision and Graph Eigenvalues
Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada +1
This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are…
Hamiltonians of Bipartite Walks
Qiuting Chen, Chris Godsil, Mariia Sobchuk +1
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like arc-reversal walks, vertex-f…
The average search probabilities of discrete-time quantum walks
Hanmeng Zhan
We study the average probability that a discrete-time quantum walk finds a marked vertex on a graph. We first show that, for a regular graph, the spectrum of the transition matrix…
Pretty good state transfer in discrete-time quantum walks
Ada Chan, Hanmeng Zhan
We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectru…
Laplacian Fractional Revival on Graphs
Ada Chan, Bobae Johnson, Mengzhen Liu +3
We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fra…
Laplacian pretty good fractional revival
Ada Chan, Bobae Johnson, Mengzhen Liu +3
We develop the theory of pretty good fractional revival in quantum walks on graphs using their Laplacian matrices as the Hamiltonian. We classify the paths and the double stars tha…
Factoring Discrete Quantum Walks on Distance Regular Graphs into Continuous Quantum Walks
Hanmeng Zhan
We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph . Given that has diameter and invertible adjacency matrix, we show that the…
Fundamentals of fractional revival in graphs
Ada Chan, Gabriel Coutinho, Whitney Drazen +6
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and…
Fractional Revival and Association Schemes
Ada Chan, Gabriel Coutinho, Christino Tamon +2
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the charact…
Perfect State Transfer on Weighted Graphs of the Johnson Scheme
Luc Vinet, Hanmeng Zhan
We characterize perfect state transfer on real-weighted graphs of the Johnson scheme . Given and $A(X) = w_0A_0 + \cd…
Perfect State Transfer in a Spin Chain without Mirror Symmetry
Gabriel Coutinho, Luc Vinet, Hanmeng Zhan +1
We introduce an analytical spin chain with asymmetrical transport properties. It has an even number of sites labeled by . It does not exhibit perfect state…
Quantum Fractional Revival on Graphs
Ada Chan, Gabriel Coutinho, Christino Tamon +2
Fractional revival is a quantum transport phenomenon important for entanglement generation in spin networks. This takes place whenever a continuous-time quantum walk maps the chara…
Quantum Walks on Embeddings
Hanmeng Zhan
We introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition mat…
A New Perspective on the Average Mixing Matrix
Gabriel Coutinho, Chris Godsil, Krystal Guo +1
We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average o…
An Infinite Family of Circulant Graphs with Perfect State Transfer in Discrete Quantum Walks
Hanmeng Zhan
We study perfect state transfer in Kendon's model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectr…
Discrete-Time Quantum Walks and Graph Structures
Chris Godsil, Hanmeng Zhan
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of gra…
Uniform Mixing on Cayley Graphs
Chris Godsil, Hanmeng Zhan
We provide new examples of Cayley graphs on which the quantum walks reach uniform mixing. Our first result is a complete characterization of all -regular Cayley graphs over…
Equiangular Lines and Covers of the Complete Graph
Gabriel Coutinho, Chris Godsil, Mirhamed Shirazi +1
The relation between equiangular sets of lines in the real space and distance-regular double covers of the complete graph is well known and studied since the work of Seidel and oth…
Perfect State Transfer in Laplacian Quantum Walk
R. Alvir, S. Dever, B Lovitz +4
For a graph and a related symmetric matrix , the continuous-time quantum walk on relative to is defined as the unitary matrix , where varies o…