Paving the way for useful computational chemistry with the orbital-optimised variational quantum eigensolver

In the past years, the capability of near-term quantum computers to address the electronic structure problem for chemical systems has been successfully demonstrated for toy-model systems such as, for example, N2, H2O and hydrogen chains Hn (n ≤ 12).

Hence, surpassing the limited availability, reliability and capacity of current quantum hardware still poses a major challenge to date and calls for the development of efficiently scaling (embedded) quantum algorithms to treat systems of real chemical relevance, such as for the purpose of optimising binding affinities in the lead-optimisation step of the small- molecule drug discovery pipeline.

To this end, we present in this contribution the Variational Quantum Eigensolver (VQE) combined with the self-consistent field (SCF) approach to orbital optimization [1]. We will discuss both a classical [2] and a quantum embedding scheme [3] based on the polarizable embedding model and density-matrix embedding theory to account for subtle effects of the environment on the electronic structure of the embedded quantum mechanical system in its ground and electronically excited states. Moreover, binding affinities are often governed by molecular interactions which necessitate to consider not only static but also dynamical electron-electron correlations. We address these challenges by making use of two distinct frameworks for VQE-SCF that can be classified as diagonalise-then-perturb [4] and perturb-and-diagonalise [5], respectively.

[1] A. Fitzpatrick, A. Nykänen, N. W. Talarico, A. Lunghi, S. Maniscalco, G. García-Pérez, and S. Knecht, arXiv:2212.11405, 2022.

[2] E. Kjellgren, W. Talarico, M. Kadek, P. Reinholdt, J. Kongsted, S. P. A. Sauer, S. Coriani and S. Knecht, manuscript in preparation, 2023.

[3] M. Kadek, R. di Remigio Eikås, G. García-Pérez, and S. Knecht, work in progress,

2023.

[4] W. Talarico, A. Fitzpatrick, R. di Remigio Eikås, G. García-Pérez, and S. Knecht, manuscript in preparation, 2023.

[5] E. Kjellgren, J. Kongsted, S. P. A. Sauer, S. Coriani and S. Knecht, work in progress,