Author

Xingwu Song

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Preprint Sep 2026

Perfect state transfer under matrix powers: parity and spectral arithmetic

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 $H^2$....

Xingwu Song · 1 citation · ⚡1

Preprint Aug 2026

Perfect State Transfer on Oriented Circulant Graphs: A Complete Classification

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