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@article{1853902,
author = {Miháliková, Ivana and Friák, Martin and Pivoluska, Matej and Plesch, Martin and Saip, Martin and Šob, Mojmír},
article_location = {SWITZERLAND},
article_number = {3},
doi = {http://dx.doi.org/10.3390/molecules27030597},
keywords = {quantum computers; hydrogen molecule; variational quantum eigensolver; circuit architecture; quantum computing; quantum chemistry; COBYLA; SPSA},
language = {eng},
issn = {1420-3049},
journal = {MOLECULES},
title = {Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule},
url = {https://www.mdpi.com/1420-3049/27/3/597},
volume = {27},
year = {2022}
}
TY - JOUR
ID - 1853902
AU - Miháliková, Ivana - Friák, Martin - Pivoluska, Matej - Plesch, Martin - Saip, Martin - Šob, Mojmír
PY - 2022
TI - Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule
JF - MOLECULES
VL - 27
IS - 3
SP - 1-15
EP - 1-15
PB - MDPI
SN - 14203049
KW - quantum computers
KW - hydrogen molecule
KW - variational quantum eigensolver
KW - circuit architecture
KW - quantum computing
KW - quantum chemistry
KW - COBYLA
KW - SPSA
UR - https://www.mdpi.com/1420-3049/27/3/597
N2 - 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.
ER -
MIHÁLIKOVÁ, Ivana, Martin FRIÁK, Matej PIVOLUSKA, Martin PLESCH, Martin SAIP and Mojmír ŠOB. Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule. \textit{MOLECULES}. SWITZERLAND: MDPI, 2022, vol.~27, No~3, p.~1-15. ISSN~1420-3049. Available from: https://dx.doi.org/10.3390/molecules27030597.
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