Recurrence in discrete-time quantum stochastic walks

Martin Štefaňák; Václav Potoček; İskender Yalçınkaya; Aurél Gábris; Igor Jex

doi:10.22331/q-2026-01-22-1982

Recurrence in discrete-time quantum stochastic walks

Martin Štefaňák¹, Václav Potoček¹, İskender Yalçınkaya¹, Aurél Gábris^1,2, and Igor Jex¹

¹Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1-Staré Město, Czech Republic
²Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, 1525 P.O. Box 49, Hungary

Published:	2026-01-22, volume 10, page 1982
Editor:	Aleksandrs Belovs
Eprint:	arXiv:2501.08674v3
Doi:	https://doi.org/10.22331/q-2026-01-22-1982
Citation:	Quantum 10, 1982 (2026).

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Abstract

Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which is a quantum stochastic process that interpolates between quantum and classical walk dynamics. Surprisingly, we find that introducing classical randomness can reduce the recurrence probability – despite the fact that the classical random walk returns with certainty – and we identify the conditions under which this intriguing phenomenon occurs. Numerical evaluation of the first-return generating function allows us to investigate the asymptotics of the return probability as the step number approaches infinity. This provides strong evidence that the suppression of recurrence probability is not a transient effect but a robust feature of the underlying quantum-classical interplay in the asymptotic limit. Our results show that for certain tasks discrete-time quantum stochastic walks outperform both classical random walks and unitary quantum walks.

Featured image: Recurrence probability as a function of stochasticity for different parameters of the quantum coin.

Popular summary

In the world of classical physics, a walker wandering randomly back and forth on a long line will always eventually return to its starting point—this is known as recurrence with certainty. In the quantum world, however, things are different; a quantum walker can use wave-like interference to spread out so quickly that it might never return.

In this paper we explore what happens when one mixes these two worlds using Discrete-Time Quantum Stochastic Walks (DTQSW). Intuitively, one might expect that adding even a little bit of classical randomness to a quantum walk would make it "more classical" and thus more likely to return home.

The Surprise: Our results demonstrate the contrary. Under certain conditions, adding classical noise actually decreases the probability of the walker returning. By interpolating between quantum and classical dynamics, we discovered a regime where the interplay of wave interference and random hopping creates a more efficient escape than either pure quantum or pure classical movement could achieve alone. This counterintuitive finding may have implications for designing more efficient quantum search algorithms and understanding how quantum information survives in noisy environments.

► BibTeX data

@article{Stefanak2026recurrencein,
  doi = {10.22331/q-2026-01-22-1982},
  url = {https://doi.org/10.22331/q-2026-01-22-1982},
  title = {Recurrence in discrete-time quantum stochastic walks},
  author = {{\v{S}}tefa{\v{n}}{\'{a}}k, Martin and Poto{\v{c}}ek, V{\'{a}}clav and Yal{\c{c}}ınkaya, {\.{I}}skender and G{\'{a}}bris, Aur{\'{e}}l and Jex, Igor},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {1982},
  month = jan,
  year = {2026}
}

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Cited by

[1] Quancheng Liu, Sabine Tornow, David A. Kessler, and Eli Barkai, "Fractionally quantized recurrence detection times in monitored quantum many-body systems", Proceedings of the National Academy of Sciences 123 22, e2529694123 (2026).

[2] Saori Yoshino, Honoka Shiratori, Tomoki Yamagami, Ryoichi Horisaki, and Etsuo Segawa, "Normal Variance Mixture with Arcsine Law of an Interpolating Walk Between Persistent Random Walk and Quantum Walk", Entropy 27 7, 670 (2025).

[3] Ammara Ammara, Václav Potoček, Martin Štefaňák, and Francesco V. Pepe, "Quantum Walk on a Line with Absorbing Boundaries", arXiv:2508.13318, (2025).

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