International Conference on Quantum Communications, Networking, and Computing (QCNC)

Quantum Walkers and Diffusion

John C Vining, Howard A. Blair

Published Mar 31, 2025• 0 citations

Abstract

Quantum walks model the behavior of a quantum state traversing a classically defined, generally finite, graph structure. This paper introduces blind quantum diffusion, a technique for evolving quantum walkers through a finite connected network without requiring global knowledge of the graph. We frame the multi-walker problem as a finite quantum cellular automaton where each vertex holds a walker at all times. These walkers will never collide as their vertex position is superpositioned by the network’s evolution and at each time step their positions update by conditioning swaps on quantum coins and partial comparators of the neighboring states. This model generates strong entanglement between vertex states providing a path toward structure independent diffusion driven by highly localized computation. We will examine some mathematical structures underlying state diffusion on arbitrary graphs such as the commutativity of operations and expected time for walkers to reach specified destinations.

DOI: 10.1109/qcnc64685.2025.00120

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