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We present a basis-set-free approach to the variational quantum eigensolverusing an adaptive representation of the spatial part of molecularwavefunctions. Our approach directly determines system-specific representationsof qubit Hamiltonians while fully omitting globally defined basis sets. In thiswork, we use directly determined pair-natural orbitals on the level ofsecond-order perturbation theory. This results in compact qubit Hamiltonianswith high numerical accuracy. We demonstrate initial applications with compactHamiltonians on up to 20 qubits where conventional representation would for thesame systems require 40-100 or more qubits.

Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach