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Explore monitored quantum hitting times and their implementation on NISQ (Noisy Intermediate-Scale Quantum) platforms in this colloquium lecture delivered by Eli Barkai from Bar Ilan University. Discover a novel time-energy uncertainty relation within monitored quantum dynamics, examining how mean recurrence times are quantized as integer multiples of sampling time and exhibit point-wise discontinuous transitions at resonances. Learn how restart mechanisms in laboratory experiments, driven by finite data collection time spans, create broadening effects on mean recurrence time transitions. Understand the proposed uncertainty relation that connects the broadening of mean hitting times near resonances to intrinsic system energies and recurrence time fluctuations. Examine experimental validation through remote experiments conducted on IBM quantum computers, and delve into fractional quantization of recurrence times for interacting spin systems using sub-space measurements. Gain insights into the theoretical foundations connecting quantum walk hitting times, restart protocols, and the statistical mechanics of quantum systems through comprehensive analysis of recent research findings and their practical applications in quantum computing platforms.
