Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach

We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wave functions. Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 22 qubits where conventional representation would for the same systems require 40-100 or more qubits. We further demonstrate reductions in the quantum circuits through the structure of the pair-natural orbitals.

Automated summary

This study introduces a basis-set-free approach for the variational quantum eigensolver, utilizing an adaptive representation of molecular wave functions to directly determine system-specific representations of qubit Hamiltonians without globally defined basis sets. The use of pair-natural orbitals at the level of second-order perturbation theory results in compact qubit Hamiltonians with high numerical accuracy. Initial applications with compact Hamiltonians on up to 22 qubits have been demonstrated, showing reductions in quantum circuits through the structure of the pair-natural orbitals.