New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)-an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.

Department of Chemistry Faculty of Science Masaryk University Kotlářská 2 CZ 611 37 Brno Czech Republic

Department of Condensed Matter Physics Faculty of Science Masaryk University Kotlářská 2 CZ 611 37 Brno Czech Republic

Institute of Computer Science Masaryk University Šumavská 416 CZ 602 00 Brno Czech Republic

Institute of Physics of Materials Czech Academy of Sciences Žižkova 22 CZ 616 62 Brno Czech Republic

Institute of Physics Slovak Academy of Sciences Dúbravská cesta 9 SK 841 04 Bratislava Slovakia

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