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arXiv · 2410.19116

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

Fabian Langkabel·Stefan Knecht·Jakob S. Kottmann
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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.

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Fabian Langkabel, Stefan Knecht, Jakob S. Kottmann. 2024-10-24. The advent of fully variational quantum eigensolvers using a hybrid multiresolution approach. https://arxiv.org/abs/2410.19116

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