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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12053 |
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| _version_ | 1866915587913940992 |
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| author | Roy, Sayan Gupta, Shamik Morigi, Giovanna |
| author_facet | Roy, Sayan Gupta, Shamik Morigi, Giovanna |
| contents | A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time interval. The optimal resetting rate can be extracted from the time evolution of the probability $S(t)$ that the detector has not clicked up to time $t$. We analyze $S(t)$ for a quantum walk on a one-dimensional lattice when the coupling between sites decays algebraically as $d^{-α}$ with the distance $d$, for $α\in(0,\infty)$. At long times, $S(t)$ decays with a universal power-law exponent that is independent of $α$. At short times, $S(t)$ exhibits a plethora of phase transitions as a function of $α$. From this, we provide a strategy to determine the optimal resetting rate. We identify two regimes: for $α>1$, the resetting rate $r$ is bounded from below by the velocity with which information propagates causally across the lattice; for $α<1$, instead, the long-range hopping tends to localize the walker: The optimal resetting rate depends on the size of the lattice and diverges as $α\to 0$. Our strategy directly connects local measurement outcomes with the global dynamics encoded in $S(t)$. We derive simple models explaining our numerical results, shedding light on the interplay of long-range coherent dynamics, symmetries, and local quantum measurement processes in determining equilibrium. Our findings offer experimentally testable predictions and provide new physical insights on optimizing quantum search through resetting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Causality, localization, and universality of monitored quantum walks with long-range hopping Roy, Sayan Gupta, Shamik Morigi, Giovanna Quantum Physics Statistical Mechanics A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time interval. The optimal resetting rate can be extracted from the time evolution of the probability $S(t)$ that the detector has not clicked up to time $t$. We analyze $S(t)$ for a quantum walk on a one-dimensional lattice when the coupling between sites decays algebraically as $d^{-α}$ with the distance $d$, for $α\in(0,\infty)$. At long times, $S(t)$ decays with a universal power-law exponent that is independent of $α$. At short times, $S(t)$ exhibits a plethora of phase transitions as a function of $α$. From this, we provide a strategy to determine the optimal resetting rate. We identify two regimes: for $α>1$, the resetting rate $r$ is bounded from below by the velocity with which information propagates causally across the lattice; for $α<1$, instead, the long-range hopping tends to localize the walker: The optimal resetting rate depends on the size of the lattice and diverges as $α\to 0$. Our strategy directly connects local measurement outcomes with the global dynamics encoded in $S(t)$. We derive simple models explaining our numerical results, shedding light on the interplay of long-range coherent dynamics, symmetries, and local quantum measurement processes in determining equilibrium. Our findings offer experimentally testable predictions and provide new physical insights on optimizing quantum search through resetting. |
| title | Causality, localization, and universality of monitored quantum walks with long-range hopping |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2504.12053 |