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QI: Fachverband Quanteninformation

QI 16: Quantum Computing Theory III

QI 16.3: Vortrag

Dienstag, 11. März 2025, 14:30–14:45, HS IV

First hitting time of a monitored quantum walk with long-range hopping — •Sayan Roy¹, Shamik Gupta², and Giovanna Morigi¹ — ¹Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany — ²Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

The time needed by a quantum walker to reach a target site on a lattice can be minimized by implementing a resetting protocol, which lets the walker restart its motion at the initial site if it did not reach the target within a certain interval. This requires monitoring the target site by means of a detector. The optimal resetting rate is intimately related to the evolution of the probability that the detector clicks. We analyse the characteristic timescales of the monitored dynamics when the coupling between sites at distance d decays algebraically as d^−α with α∈(0,∞) and the dynamics induced by the detector is encompassed by a non-Hermitian Hamiltonian. Our study allows to determine the optimal resetting time as a function of α. We identify three different behaviors: For α>2, the optimal resetting time can be understood in terms of the walker’s wave packet propagating causally towards the target: Resetting faster this characteristic time will localize the walker about the initial site giving rise to an effective Zeno-effect. For α∈(1/2,2), the optimal resetting time decreases monotonously with the lattice size and finally for α∈(0, 1/2), convergence is warranted only by continuously resetting, thereby realizing a dynamics that is reminiscent of an anti-Zeno effect.

Keywords: quantum search; quantum walk; resetting