Mixed graphs, which generalize both undirected and directed graphs, provide a natural framework for investigating a broader class of quantum transport phenomena, including perfect state transfer ($\mathrm{PST}$) and multiple state transfer ($\mathrm{MST}$). The Hermitian adjacency matrix, incorporating both symmetric a...
For perfect state transfer (PST) on unweighted mixed graphs, we classify the normalized transfer times of complete PST classes. A finite set $\Lambda\subset\mathbb R/\mathbb Z$ containing zero occurs at a nonstationary periodic vertex if and only if $\cos(2\pi(x-y))\in\mathbb Q$ for all $x,y\in\Lambda$. Every admissibl...
For a real symmetric matrix $H$ and distinct vertices $a,b$, we classify exponents $k$ for which $H^k$ has perfect state transfer (PST) from $a$ to $b$. If their supported eigenvalues are integer multiples of a common positive number, every odd exponent reduces to $H$ and every positive even exponent reduces to $H^2$....
The continuous-time quantum walk on an oriented circulant graph is determined by the Fourier eigenvalues of its Hermitian adjacency matrix. We classify perfect state transfer (PST) between distinct vertices in every nonempty oriented circulant graph. We show that each such graph is described by an odd primitive quadrat...
Xingwu Song· 0 citations
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