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Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach
Abstract
We study disorder-free localization in a spin-coupled quantum walk on the hypercube within the quantum Bernoulli noises framework. We derive a general criterion for disorder-free localization: it occurs if and only if some spectral subspace of a reduced unitary evolution contains a vector whose position marginal probability is non-uniform. For the Grover walk with distance-dependent coupling ϕσ=|σ|π/(n+1) in dimension d=4, we explicitly construct a non-uniform fixed point in the all +1 spin configuration. This implies that disorder-free localization occurs in our model.
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BibTeX
@misc{wang2026spectral,
title = {{Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach}},
author = {Ce Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07267},
eprint = {2609.07267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07267},
}
RIS
TY - UNPB
TI - Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach
AU - Ce Wang
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07267
UR - https://arxiv.org/abs/2609.07267
AB - We study disorder-free localization in a spin-coupled quantum walk on the hypercube within the quantum Bernoulli noises framework. We derive a general criterion for disorder-free localization: it occurs if and only if some spectral subspace of a reduced unitary evolution contains a vector whose position marginal probability is non-uniform. For the Grover walk with distance-dependent coupling ϕ_σ=|σ|π/(n+1) in dimension d=4, we explicitly construct a non-uniform fixed point in the all +1 spin configuration. This implies that disorder-free localization occurs in our model.
ER -