Hanmeng Zhan

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math.CO2026

Laziness of Quantum Walks on Graphs

Amulya Mohan, Christino Tamon, Yichi Xu +1

The trace of the average mixing matrix of a quantum walk measures the "laziness" of the walk: the higher the trace, the more likely that the walker returns home in the long run. In…

math.CO2026

Uniform Mixing in Chiral Quantum Walks

Luke Levine, Jessy Jacob Mesapam, Benjamin Mustico +3

This paper studies uniform mixing in continuous-time quantum walks. We show that for some unitary signing $σ$ , the complete graph $K_{n}^{σ}$ has probabilistic uniform mixing. In contr…

math.CO2024

Discrete Quantum Walks with Marked Vertices and Their Average Vertex Mixing Matrices

Amulya Mohan, Hanmeng Zhan

We study the discrete quantum walk on a regular graph $X$ that assigns negative identity coins to marked vertices $S$ and Grover coins to the unmarked ones. We find combinatorial b…

math.CO2023

$ε$ -Uniform Mixing in Discrete Quantum Walks

Hanmeng Zhan

We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoi…

Laziness of Quantum Walks on Graphs

Uniform Mixing in Chiral Quantum Walks

Discrete Quantum Walks with Marked Vertices and Their Average Vertex Mixing Matrices

ε-Uniform Mixing in Discrete Quantum Walks

$ε$ -Uniform Mixing in Discrete Quantum Walks