Quantum Information Driven Ansatz (QIDA): shallow-depth empirical quantum circuits from Quantum Chemistry

Understand

Hardware-efficient empirical variational ans\"atze for Variational Quantum Eigensolver simulations of Quantum Chemistry suffer from the lack of a direct connection to classical Quantum Chemistry methods.

• In the present work, we propose a method to fill this gap by introducing a new approach for constructing variational quantum circuits, leveraging quantum mutual information associated with classical Quantum Chemistry states to design simple yet effective heuristic ans\"atze with a topology that reflects the correlations of the molecular system.
• As first step, Quantum Chemistry calculations, such as M{\o}ller-Plesset (MP2) perturbation theory, firstly provide an approximate Natural Orbitals basis, which has been recently shown to be the best candidate one-electron basis for developing compact empirical wavefunctions (Ratini, et al 2023).
• Secondly, throughout the evaluation of quantum mutual information matrices, they provide information about the main correlations between qubits of the quantum circuit, enabling the development of a direct design of entangling blocks for the circuit.