2005/07/21 by Norio Inui, Norio Konno, Etsuo Segawa · 13 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.1103/physreve.72.056112
16 pages, 3 figures
arxiv created 2005/07/21 · openalex publication_date 2005/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the three-state quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to these two degrees of freedom, it is allowed to stay at the same position. We calculate rigorously the wave function of the particle starting from the origin for any initial qubit state and show the spatial distribution of probability of finding the particle. In contrast with the Hadamard walk with two inner states on a line, the probability of finding the particle at the origin does not converge to zero even after infinite time steps except special initial states. This implies that the particle is trapped near the origin after a long time with high probability.