Next Article in Journal
Effects of rAmb a 1-Loaded PLGA-PEG Nanoparticles in a Murine Model of Allergic Conjunctivitis
Previous Article in Journal
Estimation of the Local Concentration of the Markedly Dense Hydroxyl Radical Generation Induced by X-rays in Water
 
 
Article

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

1
Institute of Physics of Materials, Czech Academy of Sciences, v.v.i., Žižkova 22, CZ-616 62 Brno, Czech Republic
2
Institute of Computer Science, Masaryk University, Šumavská 416, CZ-602 00 Brno, Czech Republic
3
Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37 Brno, Czech Republic
4
Department of Chemistry, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37 Brno, Czech Republic
5
Institute of Physics, Slovak Academy of Sciences, Dúbravská Cesta 9, SK-841 04 Bratislava, Slovakia
*
Author to whom correspondence should be addressed.
Academic Editor: Liudmil Antonov
Molecules 2022, 27(3), 597; https://doi.org/10.3390/molecules27030597
Received: 2 December 2021 / Revised: 13 January 2022 / Accepted: 14 January 2022 / Published: 18 January 2022
(This article belongs to the Section Physical Chemistry)
Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi–Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder–Mead and Powell methods. The results obtained when using the Ry variational form were better than those obtained when the RyRz form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight. View Full-Text
Keywords: quantum computers; hydrogen molecule; variational quantum eigensolver; circuit architecture; quantum computing; quantum chemistry; COBYLA; SPSA quantum computers; hydrogen molecule; variational quantum eigensolver; circuit architecture; quantum computing; quantum chemistry; COBYLA; SPSA
Show Figures

Figure 1

MDPI and ACS Style

Miháliková, I.; Friák, M.; Pivoluska, M.; Plesch, M.; Saip, M.; Šob, M. Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule. Molecules 2022, 27, 597. https://doi.org/10.3390/molecules27030597

AMA Style

Miháliková I, Friák M, Pivoluska M, Plesch M, Saip M, Šob M. Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule. Molecules. 2022; 27(3):597. https://doi.org/10.3390/molecules27030597

Chicago/Turabian Style

Miháliková, Ivana, Martin Friák, Matej Pivoluska, Martin Plesch, Martin Saip, and Mojmír Šob. 2022. "Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule" Molecules 27, no. 3: 597. https://doi.org/10.3390/molecules27030597

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop