The advent of fully variational quantum eigensolvers using a hybrid multiresolution approach

In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis sets. Especially in quantum computation, these model chemistries are far from an accurate description of the initial electronic Hamiltonian. This work demonstrates a fully variational approach to the electronic structure problem by optimizing the orbitals that represent the second-quantized Hamiltonian, alongside a quantum circuit that generates the many-electron wavefunction. To this end, the orbitals are represented within an adaptive multi-wavelet format, guaranteeing numerical precision. We then present explicit numerical protocols and highlight the quantum circuit's role in determining the optimal orbital basis.