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Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy

João V. Cordeiro1, Eduardo I. Duzzioni2, and Edgard P. M. Amorim1,*

  • *Contact author: edgard.amorim@udesc.br
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Phys. Rev. A 114, 012459 – Published 24 July, 2026

DOI: https://doi.org/10.1103/p4pl-rvdh

Abstract

We investigate the quantum transport of delocalized states in continuous-time quantum walks (CTQWs) on a one-dimensional lattice containing a single defect. The defect is modeled by assigning complex-valued hopping amplitudes to the edges that connect the site corresponding to the mean position of the delocalized initial state to its nearest neighbors. We find that this single defective site is sufficient to enhance the ballistic spreading of an initially Gaussian wave packet. Extending these results, we implement a time-dependent alternation protocol between two distinct defect configurations, each individually yielding poor propagation of the state. The combination of these two unfavorable configurations improves the transport efficiency of the quantum walker, revealing a manifestation of Parrondo's paradox in CTQWs with delocalized initial states. This study provides insights into the role of complex-phase defects and time-dependent protocols in CTQWs, demonstrating that the interplay between quantum interference and graph engineering can effectively enhance quantum transport in discrete lattices.

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Outline

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Phys. Rev. A 114, 012459– Published 24 July, 2026
  • Received 11 November 2025
  • Revised 2 April 2026
  • Accepted 30 June 2026
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