2015/03/21 by Hao Luo, Peng Xue, Luo, Hao +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.1503.06293
openalex publication_date 2015/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena by performing a detailed numerical study of discrete-time quantum walks. In one dimension (1D), we compute the structure of the probability distribution, which is not a smooth curve but shows oscillatory features on all length scales. By analyzing walks up to N = 1000000 steps, we discuss the scaling characteristics and limiting forms of the QW in both real and Fourier space. In 2D, with a view to ready experimental realization, we consider two types of QW, one based on a four-faced coin and the other on sequential flipping of a single two-faced coin. Both QWs may be generated using two two-faced coins, which in the first case are completely unentangled and in the second are maximally entangled. We draw on our 1D results to characterize the properties of both walks, demonstrating maximal speed-up and emerging semi-classical behavior in the maximally entangled QW.