UVictoria Discrete Math Seminar: Hermie Monterde

A network of interacting qubits (usually subatomic particles) can be modelled by a connected weighted undirected graph $G$. The vertices and edges of $G$ represent the qubits and their interactions in the network, respectively. Quantum mechanics dictate that the evolution of the quantum system determined by $G$ over time is completely described by the unitary matrix $U(t)=\exp(itA)$, where $A$ is the adjacency matrix of $G$. Here, we interpret the modulus of the $(u,v)$ entry of $U(t)$ as the probability that the quantum state at vertex $u$ is found in $v$ at time $t$. In this talk, we discuss how the algebraic and spectral properties of a graph influence its ability to perform quantum state transfer.