Natural orbitals and sparsity of quantum mutual information

TL;DR

This paper demonstrates that natural orbitals are optimal for describing electron correlation in quantum chemistry, as they lead to maximally sparse quantum mutual information matrices, simplifying the representation of electron interactions.

Contribution

The study shows that natural orbitals yield maximally sparse quantum mutual information matrices, optimizing the basis for electron correlation in quantum computing applications.

Findings

Natural orbitals coincide with converged orbitals in studied molecules.

Quantum mutual information matrices are maximally sparse in natural orbitals.

Correlation is encoded in fewer qubit pairs with natural orbitals.

Abstract

Natural orbitals, defined in electronic structure and quantum chemistry as the (molecular) orbitals diagonalizing the one-particle reduced density matrix of the ground state, have been conjectured for decades to be the perfect reference orbitals to describe electron correlation. In the present work we applied the Wavefunction-Adapted Hamiltonian Through Orbital Rotation (WAHTOR) method to study correlated empirical ans\"atze for quantum computing. In all representative molecules considered, we show that the converged orbitals are coinciding with natural orbitals. Interestingly, the resulting quantum mutual information matrix built on such orbitals is also maximally sparse, providing a clear picture that such orbital choice is indeed able to provide the optimal basis to describe electron correlation. The correlation is therefore encoded in a smaller number of qubit pairs contributing to the quantum mutual information matrix.