Mainz 2026 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 67: Poster – Quantum Information
Q 67.26: Poster
Thursday, March 5, 2026, 17:00–19:00, Philo 2. OG
First-detection return statistics in quantum walks with long-range hopping — •Sayan Roy1, Shamik Gupta2, Giovanna Morigi1, and Gabriele Perfetto3 — 1Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany — 2Department of Theoretical Physics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai, 400005, India — 3Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland
Quantum walks are paradigms for many-body dynamics and are analog realization of quantum algorithms such as the quantum search. Key characterizing concepts are quantum recurrence, which describes the ability of a quantum walker to return to its initial state, and the associated first-detection time, which is the time interval elapsed between the initial time and the recurrence. In this work, we analyze a quantum walk on a chain with long-range hopping , where the coupling between sites at distance d decays as d−α, with α ≥ 0. The walker evolves unitarily between stroboscopic projective measurements on the initial site performed at times tn = n τ, n∈ N. Our study shows that the nature of the walk is controlled by the hopping exponent α. In the strong long-range regime α < 1, interference tends to localize the walker and the quantum walks are recurrent: the walker returns to the origin with probability one. For α >1, instead, the first-detection probability decays algebraically, with exponent depending on α, leading to a transient quantum walk. We connect these behaviors with the spectral features of the model.
Keywords: Quantum Walks; Quantum Search; Quantum Stochastic Process