Algebraic Graph Theory-Yujia Shi

 In a quantum state transfer problem, adding identical weighted self-loops to the endpoints of a path can improve the transfer fidelity, a phenomenon known as asymptotic state transfer. When the transfer time is chosen as t = pi / (lambda1 - lambda2), one can compute a lower bound on the fidelity between the two endpoints that depends only on the loop weights. A larger loop weight ensures higher fidelity but also increases the readout time. In the work of Chen, Mereau, and Feder, the path is modified by adding weighted edges to the third and third-from-last vertices, which achieves asymptotic state transfer between the endpoints in a shorter time. In this talk, I will present a variation in which weighted loops are added to the neighbors of the endpoints instead. This modification produces a pair of eigenvectors localized at the end vertices, and unlike in the previous cases, the difference between their corresponding eigenvalues grows more slowly. It provides an explanation for the shorter transfer time observed in this setting.

This is a joint work with Gabor Lippner