Quantum walks on random lattices : Diffusion, localization, and the absence of parametric quantum speedup

Loading...
Thumbnail Image

Access rights

openAccess

URL

Journal Title

Journal ISSN

Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2023-04

Major/Subject

Mcode

Degree programme

Language

en

Pages

12
1-12

Series

PHYSICAL REVIEW RESEARCH, Volume 5, issue 2

Abstract

Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms, and quantum simulation of condensed-matter systems. The key property of quantum walks, which lies at the heart of their quantum information applications, is the possibility for a parametric quantum speedup in propagation compared to classical random walks. In this work we study propagation of quantum walks on percolation-generated two-dimensional random lattices. In large-scale simulations of topological and trivial split-step walks, we identify distinct prediffusive and diffusive behaviors at different timescales. Importantly, we show that even arbitrarily weak concentrations of randomly removed lattice sites give rise to a complete breakdown of the superdiffusive quantum speedup, reducing the motion to ordinary diffusion. By increasing the randomness, quantum walks eventually stop spreading due to Anderson localization. Near the localization threshold, we find that the quantum walks become subdiffusive. The fragility of quantum speedup implies dramatic limitations for quantum information applications of quantum walks on random geometries and graphs.

Description

Funding Information: The authors acknowledge the Academy of Finland for support (Grant No. 331094). Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Keywords

Other note

Citation

Duda, R, Ivaki, M N, Sahlberg, I, Pöyhönen, K & Ojanen, T 2023, ' Quantum walks on random lattices : Diffusion, localization, and the absence of parametric quantum speedup ', PHYSICAL REVIEW RESEARCH, vol. 5, no. 2, 023150, pp. 1-12 . https://doi.org/10.1103/PhysRevResearch.5.023150