Quantum Information\nDriven Ansatz (QIDA): Shallow-Depth\nEmpirical Quantum Circuits from Quantum Chemistry

Hardware-efficient empirical variational ansätze\nfor Variational\nQuantum Eigensolver (VQE) simulations of quantum chemistry often lack\na direct connection to classical quantum chemistry methods. In this\nwork, we propose a method to bridge this gap by introducing a novel\napproach to constructing a starting point for variational quantum\ncircuits, leveraging quantum mutual information from classical quantum\nchemistry states to design simple yet effective heuristic ansätze\nwith a topology reflecting the molecular system’s correlations.\nAs a first step, we make use of quantum chemistry calculations, such\nas Mo̷ller–Plesset (MP2) perturbation theory, to initially\nprovide approximate Natural Orbitals, which have been shown to be\nthe best candidate one-electron basis for developing compact empirical\nwave functions.<sup>1</sup> Second, we evaluate the quantum mutual\ninformation matrix, which provides insights about the main correlations\nbetween qubits of the quantum circuit, and enables a direct design\nof entangling blocks for the circuit. The resulting ansatz is then\nused with a VQE to obtain a short-depth variational ground state of\nthe electronic Hamiltonian. To validate our approach, we perform a\ncomprehensive statistical analysis through simulations of various\nmolecular systems (<i>H</i><sub>2</sub>, <i>LiH</i>, <i>H</i><sub>2</sub><i>O</i>) and apply it\nto the more complex <i>NH</i><sub>3</sub> molecule. The\nreported results demonstrate that the proposed methodology gives rise\nto highly effective ansätze, outperforming the standard empirical\nladder-entangler ansatz. Overall, our approach can be used as an effective\nstate preparation, providing a promising route for designing efficient\nvariational quantum circuits for large molecular systems.