  By utilizing quantum mechanical effects, such as superposition and
entanglement, quantum metrology promises higher precision than the classical
strategies. It is, however, practically challenging to realize the quantum
advantages. This is mainly due to the difficulties in engineering non-classical
probe state and performing nontrivial measurement in practise, particularly
with a large number of particles. Here we propose a scalable scheme with a
symmetrical variational quantum circuit which, same as the Loschmidt echo,
consists of a forward and a backward evolution. We show that in this scheme the
quantum Fisher information, which quantifies the precision limit, can be
efficiently obtained from a measurement signal of the Loschmidt echo. We
experimentally implement the scheme on an ensemble of 10-spin quantum processor
and successfully achieves a precision near the theoretical limit which
outperforms the standard quantum limit with 12.4 dB. The scheme can be
efficiently implemented on various noisy intermediate-scale quantum devices
which provides a promising routine to demonstrate quantum advantages.
