  In open quantum systems, the precision of metrology inevitably suffers from
the noise. {In Markovian open quantum dynamics, the precision can not be
improved by using entangled probes although the measurement time is effectively
shortened.} However, it was predicted over one decade ago that in a
non-Markovian one, the error can be significantly reduced by the quantum Zeno
effect (QZE) [Chin, Huelga, and Plenio, Phys. Rev. Lett. \textbf{109}, 233601
(2012)]. In this work, we apply a recently-developed quantum simulation
approach to experimentally verify that entangled probes can improve the
precision of metrology by the QZE. Up to $n=7$ qubits, we demonstrate that the
precision has been improved by a factor of $n^{1/4}$, which is consistent with
the theoretical prediction. Our quantum simulation approach may provide an
intriguing platform for experimental verification of various quantum metrology
schemes.
