2003/09/07 by Daniel Shapira, Ofer Biham, A. J. Bracken +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Crossover #Gaussian #Mathematical physics #Mathematics #Noise (video) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum mechanics #Quantum walk #Random walk #Sigma #Statistical physics #Statistics #Unitary state #quant-ph
paper · pdf · doi:10.1103/physreva.68.062315
28 pages, 12 figures
arxiv created 2003/09/07 · openalex publication_date 2003/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, \ensuremathσ(t) scales as \ensuremathσ(t)\ensuremath∼t, unlike the classical random walk for which \ensuremathσ(t)\ensuremath∼√(t). It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be T\ensuremath∼\ensuremathα^\ensuremath-2, where \ensuremathα is the standard deviation of the noise.