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arXiv:2610.14467

Harmonic Reduction of Spin-Coupled Grover Walks on Hypercubes via Quantum Bernoulli Noises

Ce Wang

quant-phmath-phmath.COmath.PRmath.RTSubmitted Oct 10, 2026• Announced Oct 13, 2026• 0 citations• Revised Oct 14, 2026 (v2)
v1 · Oct 10, 2026v2 · Oct 14, 2026
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Abstract

We consider spin-coupled Grover walks on hypercubes within the framework of quantum Bernoulli noises (QBN). We identify parity-dependent harmonic subspaces generated by the central Hamming layers: in even dimension they give a fixed-point subspace, whereas in odd dimension the walk reduces on the harmonic subspace to an explicit eight-dimensional reduced dynamics. Using symmetric-group representation theory, we characterize the corresponding isotypic structure and determine the reduced spectrum. The harmonic reduction also yields explicit long-time probability behavior and shows that the resulting states may occupy an asymptotically vanishing fraction of the hypercube while still spanning its full Hamming diameter.

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