Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach

• URL: http://arxiv.org/abs/2609.07267v1
• Date: Mon, 07 Sep 2026 09:25:47 GMT
• Title: Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach
• Abstract summary: We study disorder-free localization in a spin-coupled quantum walk on the hypercube within the quantum Bernoulli noises framework.<n>We explicitly construct a non-uniform fixed point in the all (+1) spin configuration.
• Score: 5.246888191460796
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \(φ_σ=|σ|π/(n+1)\) 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.

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