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

J 2022

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

MIHÁLIKOVÁ, Ivana, Martin FRIÁK, Matej PIVOLUSKA, Martin PLESCH, Martin SAIP et. al.

Basic information

Original name

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

Authors

MIHÁLIKOVÁ, Ivana (703 Slovakia, belonging to the institution), Martin FRIÁK (203 Czech Republic, belonging to the institution), Matej PIVOLUSKA (703 Slovakia, belonging to the institution), Martin PLESCH (703 Slovakia, belonging to the institution), Martin SAIP (203 Czech Republic, belonging to the institution) and Mojmír ŠOB (203 Czech Republic, guarantor, belonging to the institution)

Edition

MOLECULES, SWITZERLAND, MDPI, 2022, 1420-3049

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10301 Atomic, molecular and chemical physics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 4.600

RIV identification code

RIV/00216224:14310/22:00125831

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.3390/molecules27030597

UT WoS

000761013800001

Keywords in English

quantum computers; hydrogen molecule; variational quantum eigensolver; circuit architecture; quantum computing; quantum chemistry; COBYLA; SPSA

Abstract

V originále

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.

Links

MUNI/G/1596/2019, interní kód MU

Name: Development of algorithms for application of quantum computers in electronic-structure calculations in solid-state physics and chemistry (Acronym: Qubits4PhysChem)

Investor: Masaryk University, INTERDISCIPLINARY - Interdisciplinary research projects

Citovat

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. MOLECULES. SWITZERLAND: MDPI, 2022, vol. 27, No 3, p. 1-15. ISSN 1420-3049. Available from: https://dx.doi.org/10.3390/molecules27030597.

@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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