Compact multi-threshold quantum information driven ansatz for strongly interactive lattice spin models

Abstract 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 ansätze. We introduce a systematic procedure for ansatz building based on approximate Quantum Mutual Information (QMI) with improvement on each layer obtained by repeated applications of the previously defined Quantum Information Driven Ansatz (QIDA) approach. The objective is to recover the correlation that is discarded by the standalone QIDA method, including it in additional layers. Our approach generates a layered-structured ansatz, where each layer entangler map is defined on the qubit couples selected based on their QMI values. Following the rationale that shallower circuits may mitigate the phenomenon of barren plateaus, the Multi-QIDA ansatz partitions the optimization landscape into smaller steps. The method employs an iterative construction and optimization strategy, progressively extending the circuit depth to guide the optimization towards the appropriate potential well. We benchmarked our approach on various configurations of the Heisenberg model Hamiltonian, ranging between 9 and 12 qubits, demonstrating significant improvements in the accuracy of the ground state energy calculations, in terms of deviation from the best results and convergence, 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.