  Quantum algorithms based on the variational principle have found applications
in diverse areas with a huge flexibility. But as the circuit size increases the
variational landscapes become flattened, causing the so-called Barren plateau
phenomena. This will lead to an increased difficulty in the optimization phase,
due to the reduction of the cost function parameters gradient. One of the
possible solutions is to employ shallower circuits or adaptive ans\"atze.
  We introduce a systematic procedure for ansatz building based on approximate
Quantum Mutual Information (QMI) with improvement on each layer based on the
previous Quantum Information Driven Ansatz (QIDA) approach. Our approach
generates a layered-structured ansatz, where each layer's qubit pairs are
selected based on their QMI values, resulting in more efficient state
preparation and optimization routines. We benchmarked our approach on various
configurations of the Heisenberg model Hamiltonian, demonstrating significant
improvements in the accuracy of the ground state energy calculations compared
to traditional heuristic ansatz methods. Our results show that the Multi-QIDA
method reduces the computational complexity while maintaining high precision,
making it a promising tool for quantum simulations in lattice spin models.
