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  • Open Access

Quantum walks: First hitting times with weak measurements

Tim Heine1,*, Eli Barkai2, Klaus Ziegler3,4, and Sabine Tornow5

  • *Contact author: tim.heine@dlr.de
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Phys. Rev. A 113, 052426 – Published 12 May, 2026

DOI: https://doi.org/10.1103/j2yb-fmw1

Abstract

We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak measurements on a dilated system, enabling minimally invasive monitoring throughout the evolution. To achieve this, we implement a weak measurement protocol theoretically and complement it with both numerical simulations and investigations on an IBM quantum computer. Despite the implementation of a generalized measurement, the proposed protocol provides a description purely within the Hilbert space of the quantum system. Our results reveal that for rank-one monitored, pure initial states, the first hitting timescales inversely with the coupling parameter between the ancilla and the quantum system.

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Phys. Rev. A 113, 052426– Published 12 May, 2026
  • Received 8 July 2025
  • Revised 2 December 2025
  • Accepted 10 April 2026
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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.

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