Discretization and topological protection of p-adic Jackiw–Rebbi zero modes

Construct the continuous-time quantum walk discretizing the p-adic Jackiw–Rebbi model and determine whether its topologically protected zero modes survive discretization on G_l^3 as noise-resilient network nodes.

Background

The paper refers to a p-adic Jackiw–Rebbi model whose Dirac Hamiltonian has localized, topologically protected zero modes. These modes are proposed as possible robust nodes for a p-adic quantum network.

The present work discretizes only the free p-adic Dirac equation. It neither constructs the corresponding walk for the Jackiw–Rebbi model nor tests whether the localized zero modes and their protection persist on the finite hierarchical graph.

References

We have not constructed the CTQW that discretizes that model, nor determined whether its zero modes survive discretization on G_{l}{3} as noise-resilient network nodes, as suggested informally in Section \ref{Section_Quantum_Computers}.

— p-Adic Dirac Equations, Continuous-Time Quantum Walks, and Quantum Networks  (2609.04358 - Zúñiga-Galindo, 3 Sep 2026) in Section 6, subsection “Open problems,” item (6) (Topological protection on the walk)