Quantum computing for classical problems: variational quantum eigensolver for activated processes
The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker–Plank–Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the d...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2021-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ac3ff9 |
| _version_ | 1797748578289975296 |
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| author | Pierpaolo Pravatto Davide Castaldo Federico Gallina Barbara Fresch Stefano Corni Giorgio J Moro |
| author_facet | Pierpaolo Pravatto Davide Castaldo Federico Gallina Barbara Fresch Stefano Corni Giorgio J Moro |
| author_sort | Pierpaolo Pravatto |
| collection | DOAJ |
| description | The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker–Plank–Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the diffusive regime and it is, therefore, a workhorse of physical chemistry. In this paper we report on the development and implementation of a variational quantum eigensolver to solve the Fokker–Planck–Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be effectively applied to classical systems, paving the way to new applications of quantum computers. We compute the conformational transition rate in a linear chain of rotors with nearest-neighbour interactions. We provide a method to encode the probability distribution for a given conformation of the chain on a quantum computer and assess its scalability in terms of operations. A performance analysis on noisy quantum emulators and quantum devices (IBMQ Santiago) is provided for a small chain which shows results in good agreement with the classical benchmark without any further addition of error mitigation techniques. |
| first_indexed | 2024-03-12T16:06:49Z |
| format | Article |
| id | doaj.art-a95795c1ce694a6c8aeeafefc2d04b30 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:06:49Z |
| publishDate | 2021-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a95795c1ce694a6c8aeeafefc2d04b302023-08-09T14:19:07ZengIOP PublishingNew Journal of Physics1367-26302021-01-01231212304510.1088/1367-2630/ac3ff9Quantum computing for classical problems: variational quantum eigensolver for activated processesPierpaolo Pravatto0https://orcid.org/0000-0002-4281-4147Davide Castaldo1https://orcid.org/0000-0001-8622-175XFederico Gallina2https://orcid.org/0000-0002-3694-6397Barbara Fresch3https://orcid.org/0000-0002-0988-0644Stefano Corni4https://orcid.org/0000-0001-6707-108XGiorgio J Moro5https://orcid.org/0000-0003-3905-3831Università degli studi di Padova , Dipartimento di Scienze Chimiche, Via Marzolo 1—35131 Padova, ItalyUniversità degli studi di Padova , Dipartimento di Scienze Chimiche, Via Marzolo 1—35131 Padova, ItalyUniversità degli studi di Padova , Dipartimento di Scienze Chimiche, Via Marzolo 1—35131 Padova, ItalyUniversità degli studi di Padova , Dipartimento di Scienze Chimiche, Via Marzolo 1—35131 Padova, Italy; Padua Quantum Technologies Research Center, Università di Padova, ItalyUniversità degli studi di Padova , Dipartimento di Scienze Chimiche, Via Marzolo 1—35131 Padova, Italy; Padua Quantum Technologies Research Center, Università di Padova, Italy; Istituto Nanoscienze—CNR , via Campi 213/A, 41125 Modena, ItalyUniversità degli studi di Padova , Dipartimento di Scienze Chimiche, Via Marzolo 1—35131 Padova, Italy; Padua Quantum Technologies Research Center, Università di Padova, ItalyThe theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker–Plank–Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the diffusive regime and it is, therefore, a workhorse of physical chemistry. In this paper we report on the development and implementation of a variational quantum eigensolver to solve the Fokker–Planck–Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be effectively applied to classical systems, paving the way to new applications of quantum computers. We compute the conformational transition rate in a linear chain of rotors with nearest-neighbour interactions. We provide a method to encode the probability distribution for a given conformation of the chain on a quantum computer and assess its scalability in terms of operations. A performance analysis on noisy quantum emulators and quantum devices (IBMQ Santiago) is provided for a small chain which shows results in good agreement with the classical benchmark without any further addition of error mitigation techniques.https://doi.org/10.1088/1367-2630/ac3ff9quantum algorithmsvariational quantum eigensolverFokker–Planck–Smoluchowski equationrate constant of activated processes |
| spellingShingle | Pierpaolo Pravatto Davide Castaldo Federico Gallina Barbara Fresch Stefano Corni Giorgio J Moro Quantum computing for classical problems: variational quantum eigensolver for activated processes New Journal of Physics quantum algorithms variational quantum eigensolver Fokker–Planck–Smoluchowski equation rate constant of activated processes |
| title | Quantum computing for classical problems: variational quantum eigensolver for activated processes |
| title_full | Quantum computing for classical problems: variational quantum eigensolver for activated processes |
| title_fullStr | Quantum computing for classical problems: variational quantum eigensolver for activated processes |
| title_full_unstemmed | Quantum computing for classical problems: variational quantum eigensolver for activated processes |
| title_short | Quantum computing for classical problems: variational quantum eigensolver for activated processes |
| title_sort | quantum computing for classical problems variational quantum eigensolver for activated processes |
| topic | quantum algorithms variational quantum eigensolver Fokker–Planck–Smoluchowski equation rate constant of activated processes |
| url | https://doi.org/10.1088/1367-2630/ac3ff9 |
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