Quantum Information Driven Ansatz (QIDA): Shallow-Depth Empirical Quantum Circuits from Quantum Chemistry

Hardware-efficient empirical variational ansatze for Variational Quantum Eigensolver (VQE) simulations of quantum chemistry often lack a direct connection to classical quantum chemistry methods. In this work, we propose a method to bridge this gap by introducing a novel approach to constructing a starting point for variational quantum circuits, leveraging quantum mutual information from classical quantum chemistry states to design simple yet effective heuristic ansatze with a topology reflecting the molecular system's correlations. As a first step, we make use of quantum chemistry calculations, such as Moller-Plesset (MP2) perturbation theory, to initially provide approximate Natural Orbitals, which have been shown to be the best candidate one-electron basis for developing compact empirical wave functions.1 Second, we evaluate the quantum mutual information matrix, which provides insights about the main correlations between qubits of the quantum circuit, and enables a direct design of entangling blocks for the circuit. The resulting ansatz is then used with a VQE to obtain a short-depth variational ground state of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis through simulations of various molecular systems (H 2, LiH, H 2 O) and apply it to the more complex NH 3 molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansatze, outperforming the standard empirical ladder-entangler ansatz. Overall, our approach can be used as an effective state preparation, providing a promising route for designing efficient variational quantum circuits for large molecular systems.