Public Research Seminar by Advanced Materials Thrust, Function Hub, HKUST(GZ) - Quantum hitting times with repeated measurements and restarts

We study quantum first-“passage” times (quantum hitting times) with restart, extending concepts in classical restart to quantum systems. Using “monitored” (repeatedly measured) quantum walks, we show how restarts eliminate dark states and expedite quantum search, revealing unique phenomena such as multiple minima in the mean hitting times and restart- induced instability. For the optimization problem, which is a practical aspect of the investigation, we find that the ballisticity of the wavefront spreading is manifested in the optimal quantum restarts, interpretable with a semi-classical picture. Those effects are essentially attributed to quantum interference, and are found mainly in but not limited to infinite quantum systems. For finite systems, previous theoretical studies expose a topological interpretation for the quantized expectation of the quantum recurrence time, with discontinuous transitions (dips) at resonances, where the system wave function partially revives, and the dark subspace expands. These transitions are exhibiting broadening effects when subjected to the restart mechanism, which is captured by a time-energy uncertainty-like relation. This relation is verified on a superconducting quantum processor, revealing the interplay between the unitary dynamics and quantum measurements, and provide practical insights for designing efficient quantum algorithms utilizing restart strategies.