Quantum Information Theory on Sparse Wave Functions and Applications for Quantum Chemistry

In recent years Quantum Computing prominently entered in the field of Computational Chemistry, importing and transforming computational methods and ideas originally developed within other disciplines, such as Physics, Mathematics and Computer Science into algorithms able to estimate quantum properties of atoms and molecules on present and future quantum devices. An important role in this contamination process is attributed to Quantum Information techniques, having the 2-fold role of contributing to the analysis of electron correlation and entanglements and guiding the construction of wave function variational ansatzes for the Variational Quantum Eigensolver technique. This paper introduces the tool SparQ (Sparse Quantum state analysis), designed to efficiently compute fundamental quantum information theory observables on post-Hartree-Fock wave functions sparse in their definition space. The core methodology involves mapping Fermionic wave functions to qubit space using Fermionic-to-qubits transformations and leveraging the sparse nature of these wave functions to evaluate observables and properties of the wave function. The effectiveness of SparQ is validated by analyzing the mutual information matrices of wave functions for the water molecule and the entropy of ∼10² qubits describing the benzene molecule. This highlights its capability to handle large-scale quantum systems, limited mainly by the capabilities of quantum chemical methods used to retrieve the wave functions. The results indicate that quantum information theoretical analysis, so far limited to traditional tensor network methods and study of transition operators, can be applied to all post-Hartree-Fock wave functions, extending their applications to larger and more complex chemical systems.