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

TL;DR

This paper introduces a fully variational quantum eigensolver that optimizes orbitals using a hybrid multiresolution approach, enhancing accuracy in electronic structure calculations.

Contribution

It presents a novel fully variational method combining orbital optimization with quantum circuits, utilizing an adaptive multi-wavelet basis for precise electronic structure modeling.

Findings

Demonstrates the effectiveness of the hybrid multiresolution approach

Shows improved accuracy over traditional fixed-basis methods

Provides explicit protocols for quantum circuit implementation

Abstract

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 \textit{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.