Eli Barkai (Bar Ilan University)

Monitored Quantum Hitting Times on NISQ Platforms

We introduce a time-energy uncertainty relation within the context of monitored quantum dynamics [1] . Previous studies have established that the mean recurrence time, which represents the time taken to return to the initial state, is quantized as an integer multiple of the sampling time, displaying point-wise discontinuous transitions at resonances. Our findings demonstrate that the natural utilization of the restart mechanism in laboratory experiments [2], driven by finite data collection time spans, leads to a broadening effect on the transitions of the mean recurrence time. Our proposed uncertainty relation captures the underlying essence of these phenomena, by connecting the broadening of the mean hitting time near resonances, to the intrinsic energies of the quantum system and to the fluctuations of recurrence time. Our uncertainty relation has also been validated through remote experiments conducted on an International Business Machines Corporation (IBM) quantum computer. We then discuss ractional quantization of the recurrence time for interacting spin systems using sub-space measurements [3].

References
[1] R. Yin, Q. Wang, S. Tornow, and E. Barkai, Restart uncertainty relation for
monitored quantum dynamics Proceedings of the National Academy of
Sciences 122 (1) e2402912121, (2025).
[2] R. Yin, E. Barkai Restart expedites quantum walk hitting times Phys. Rev.
Lett. 130, 050802 (2023).
[3] Q. Liu, S. Tornow, D. Kessler, and E. Barkai Fractionally Quantized Recurrence
Detection Times in Monitored Quantum Many-Body Systems Proceedings of
the National Academy of Sciences 123 (22) e2529694123 (2026).