2020/07/02 by Norio Konno, Konno, Norio, Kaname Matsue +3 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #FOS: Physical sciences #Gaussian #Heterogeneous random walk in one dimension #Mathematical Physics (math-ph) #Mathematics #Measure (data warehouse) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum algorithm #Quantum decoherence #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #Random walk #Statistical physics #Statistics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.2007.00940
published in arXiv (Cornell University) (Cornell University) · 30 pages
arxiv created 2020/07/02 · openalex publication_date 2020/07/02 · arxiv updated 2020/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
We propose an intermediate walk continuously connecting an open quantum random walk and a quantum walk with parameters M∈ ℕ controlling a decoherence effect; if M=1, the walk coincides with an open quantum random walk, while M=∞, the walk coincides with a quantum walk. We define a measure which recovers usual probability measures on ℤ for M=∞ and M=1 and we observe intermediate behavior through numerical simulations for varied positive values M. In the case for M=2, we analytically show that a typical behavior of quantum walks appears even in a small gap of the parameter from the open quantum random walk. More precisely, we observe both the ballistically moving towards left and right sides and localization of this walker simultaneously. The analysis is based on Kato's perturbation theory for linear operator. We futher analyze this limit theorem in more detail and show that the above three modes are described by Gaussian distributions.