Compact Multi-Threshold Quantum Information Driven Ansatz For Strongly Interactive Lattice Spin Models

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.