Natural orbitals and sparsity of quantum mutual information

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 ansätze 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.

arXiv comment11 pages + supplementary meterial

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• Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization
• Quantum information theory on sparse wavefunctions and applications for Quantum Chemistry