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

In electronic structure theory, variational computing offers a valuable paradigm for the approximation of electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in predefined 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 variationally optimizing the orbitals representing 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 showcase explicit numerical protocols and highlight the quantum circuit’s effects on determining the optimal orbital basis.