First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States
arxiv(2024)
摘要
We investigate a quantum walk on a ring represented by a directed triangle
graph with complex edge weights and monitored at a constant rate until the
quantum walker is detected. To this end, the first hitting time statistics is
recorded using unitary dynamics interspersed stroboscopically by measurements,
which is implemented on IBM quantum computers with a midcircuit readout option.
Unlike classical hitting times, the statistical aspect of the problem depends
on the way we construct the measured path, an effect that we quantify
experimentally. First, we experimentally verify the theoretical prediction that
the mean return time to a target state is quantized, with abrupt
discontinuities found for specific sampling times and other control parameters,
which has a well-known topological interpretation. Second, depending on the
initial state, system parameters, and measurement protocol, the detection
probability can be less than one or even zero, which is related to dark-state
physics. Both, return-time quantization and the appearance of the dark states
are related to degeneracies in the eigenvalues of the unitary time evolution
operator. We conclude that, for the IBM quantum computer under study, the first
hitting times of monitored quantum walks are resilient to noise. Yet, a finite
number of measurements leads to broadening effects, which modify the
topological quantization and chiral effects of the asymptotic theory with an
infinite number of measurements. Our results point the way for the development
of novel quantum walk algorithms that exploit measurement-induced effects on
quantum computers.
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