Quantum State Routing and Perfect State Transfer on Signed Graphs under Environmental Noise

Abstract:Routing unknown quantum information across distributed communication networks requires autonomous, measurement-free mechanisms to prevent wave-function collapse. Szegedy quantum walks provide a mechanism for spatial state transport. The conventional walks on unweighted graphs suffer from severe back-reflection, spatial dispersion, and channel crosstalk. In this paper, we introduce a deterministic topological quantum routing architecture based on coined Szegedy quantum walks on edge-duplicated signed graphs. By treating edge signs as localized phase shifts within a balanced coin reflection, we enforce an exact zero back-scattering condition across routing nodes. We demonstrate deterministic Perfect State Transfer (PST) with unit fidelity at exact arrival times across fundamental archetypes, including the signed dumbbell switch $D_{2m,0,2n}$ and scalable glued binary trees. Furthermore, we analyse routing performance under realistic open-system amplitude and phase damping noise channels.

Comments are welcome! This version of the manuscript was prepared in a hurry to meet a deadline

Quantum Physics (quant-ph); Discrete Mathematics (cs.DM); Information Theory (cs.IT); Combinatorics (math.CO)

arXiv:2609.39890 [quant-ph]

(or arXiv:2609.39890v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.39890 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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