  We present a basis-set-free approach to the variational quantum eigensolver
using an adaptive representation of the spatial part of molecular
wavefunctions. 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 20 qubits where conventional representation would for the
same systems require 40-100 or more qubits.
