  Variational quantum algorithms have been widely demonstrated in both
experimental and theoretical contexts to have extensive applications in quantum
simulation, optimization, and machine learning. However, the exponential growth
in the dimension of the Hilbert space results in the phenomenon of vanishing
parameter gradients in the circuit as the number of qubits and circuit depth
increase, known as the barren plateau phenomena. In recent years, research in
non-equilibrium statistical physics has led to the discovery of the realization
of many-body localization. As a type of floquet system, many-body localized
floquet system has phase avoiding thermalization with an extensive parameter
space coverage and have been experimentally demonstrated can produce time
crystals. We applied this circuit to the variational quantum algorithms for the
calculation of many-body ground states and studied the variance of gradient for
parameter updates under this circuit. We found that this circuit structure can
effectively avoid barren plateaus. We also analyzed the entropy growth,
information scrambling, and optimizer dynamics of this circuit. Leveraging this
characteristic, we designed a new type of variational ansatz, called the
'many-body localization ansatz'. We applied it to solve quantum many-body
ground states and examined its circuit properties. Our numerical results show
that our ansatz significantly improved the variational quantum algorithm.
