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

Hardware-efficient empirical variational ansätze 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 ansätze with a topology reflecting the molecular system's correlations. As a first step, we make use of quantum chemistry calculations, such as Mo̷ller-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 (<i>H</i>₂, <i>LiH</i>, <i>H</i>₂<i>O</i>) and apply it to the more complex <i>NH</i>₃ molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, 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.