Symmetric quantum walks on Hamming graphs and their limit distributions

• URL: http://arxiv.org/abs/2509.26243v1
• Date: Tue, 30 Sep 2025 13:36:34 GMT
• Title: Symmetric quantum walks on Hamming graphs and their limit distributions
• Authors: Robert C. Griffiths, Shuhei Mano,
• Abstract summary: We study a class of symmetric quantum walks on Hamming graphs.<n> Eigenvalues of the unitary operator of the walks are zeros of certain self-reciprocals.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the literature. Eigenvalues of the unitary operator of the quantum walks are zeros of certain self-reciprocal polynomials. We obtain a spectral representation of the wave vector, where our systematic treatment relies on the coin space isomorphic to the state space and the commutative association scheme. The limit distributions of several quantum walks are obtained.

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