6 papers · 1 filter
Optimal and Deterministic Quantum Search on the Simplex of Complete Graphs
Kiyoji Huang Fujiwara, Yujia Shi, Thomas G. Wong
The simplex of complete graphs, also known as the first-order truncated simplex lattice, is a network of identical complete graphs, each with vertices, such that each cli…
Self-Trapping Bounds for Continuous-Time Nonlinear Quantum Walks on Path and Cycle Graphs
Yujia Shi, Thomas G. Wong
We explore a continuous-time quantum walk starting at a single vertex on the discrete path and cycle with a cubic nonlinearity. Such nonlinearities arise in Bose-Einstein condensat…
Fast state transfer via loop weights
Gabor Lippner, Yujia Shi
We prove that almost-linear-time high-fidelity state transfer is achievable in a quantum spin chain using loop weights at the second and second-to-last nodes. We provide specific p…
Continuous-Time Quantum State Transfer with a Generalized Laplacian
Yujia Shi
Quantum walks generated by the adjacency matrix or the Laplacian are known to exhibit low transfer fidelity on general graphs. In this paper, we study continuous-time quantum walks…
Strong quantum state transfer on graphs via loop edges
Gabor Lippner, Yujia Shi
We quantify the effect of weighted loops at the source and target nodes of a graph on the strength of quantum state transfer between these vertices. We give lower bounds on loop we…
Quantifying State Transfer Strength on Graphs with Involution
Gabor Lippner, Yujia Shi
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltoni…