The (standard) average mixing matrix of a continuous-time quantum walk is computed by
taking the expected value of the mixing matrices of the walk under the uniform sampling …

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 of …

We study the diagonal entries of the average mixing matrix of continuous quantum walks.
The average mixing matrix is a graph invariant; it is the sum of the Schur squares of spectral …

The Szegedy quantum walk is a discrete time quantum walk model which defines a quantum
analogue of any Markov chain. The long-term behavior of the quantum walk can be encoded …

We analyze continuous-time quantum walks on necklace graphs—cyclical graphs consisting
of many copies of a smaller graph (pearl). Using a Bloch-type ansatz for the eigenfunctions …

The fundamental problem of sampling from the limiting distribution of quantum walks on
networks, known as mixing, finds widespread applications in several areas of quantum …

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of
applications. Likewise, random walks on graphs are a fundamental building block for a large …

The quantum mixing time is a critical factor affecting the efficiency of quantum sampling and
algorithm performance. It refers to the minimum time required for a quantum walk to …

A classical lazy random walk on cycles is known to mix with the uniform distribution. In
contrast, we show that a continuous-time quantum walk on cycles exhibits strong non …

If X is a graph with adjacency matrix A, then we define H (t) to be the operator exp (it A). The
Schur (or entrywise) product H (t)∘ H (− t) is a doubly stochastic matrix and because of work …