2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90198In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetry of probability distributions for the Hadamard walk.17 pages, revised version, Journal-ref addedQuantum Physicstext