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Strong Decay of Correlations for Gibbs States in Any Dimension

Capel Cuevas, Angela, Andreas Blühm, Pérez-Hernández, Antonio

Published Jul 26, 2024• 0 citations
OpenAlex

Abstract

Acknowledgements: AB acknowledges financial support from the European Research Council (ERC Grant Agreement No. 81876) and VILLUM FONDEN via the QMATH Centre of Excellence (Grant No.10059). Moreover, AB is supported by the French National Research Agency in the framework of the “France 2030” program (ANR-11-LABX-0025-01) for the LabEx PERSYVAL. AC acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 470903074 – TRR 352. APH is partially supported by the Escuela Técnica Superior de Ingenieros Industriales (UNED) of Spain, project 2023-ETSII-UNED-01, as well as by the Spanish Ministerio de Ciencia e Innovación project PID2020-113523GB-I00 and by Comunidad de Madrid project QUITEMAD-CM P2018/TCS4342. AC and AB are grateful for the hospitality of Perimeter Institute where part of this work was carried out. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. This research was also supported in part by the Simons Foundation through the Simons Foundation Emmy Noether Fellows Program at Perimeter Institute.

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A quantum computer exhibits quantum advantage when it can perform a calculation that a classical computer is unable to complete. It follows that a company with a quantum computer would be a monopolist in the market for such a calculation if its only competitor was a company with a classical computer. Conversely, economic outcomes are unclear if quantum computers do not exhibit a quantum advantage, but classical and quantum computers have different cost structures. We model a Cournot duopoly where a quantum computing company competes against a classical computing company. The model features an asymmetric variable cost structure between the two companies and the potential for an asymmetric fixed cost structure, where each firm can invest in scaling its hardware to expand its respective market. We find that even if (1) the companies can complete identical calculations, and thus there is no quantum advantage, and (2) it is more expensive to scale the quantum computer, the quantum computing company may be more profitable and also invest more in market creation due to efficiency gains from using quantum algorithms. Finally, we provide examples of settings where the classical computer can also perform a calculation, but not in a cost-effective enough manner to be commercially viable. In such a setting, the quantum computing company becomes a monopolist despite exhibiting no quantum advantage. Taken together, quantum computers may not need to display a quantum advantage to be able to generate a quantum economic advantage for the companies that deploy them. This paper was accepted by D. J. Wu, information systems. Funding: R. G. Melko is supported by the Natural Sciences and Engineering Research Council of Canada, Canada Research Chair program, and the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. A. Goldfarb is supported by the Sloan Foundation and the Social Sciences and Humanities Council of Canada. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4578 .

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All data for the preprint "Observation of many-body dynamical localization" The Innsbruck team acknowledges funding by a Wittgenstein prize grant under Austrian Science Fund (FWF) project number Z336-N36, by the European Research Council (ERC) under project number 789017, by an FFG infrastructure grant with project number FO999896041, and by the FWF's COE 1 and quantA . MH thanks the doctoral school ALM for hospitality, with funding from the FWF under the project number W1259-N27.The team at Zhejiang University is supported by the National Natural Science Foundation of China (Grant No. 12375021) and the National Key R\&D Program of China (Grant No. 2022YFA1404203).HY is also supported by the Swiss National Science Foundation under grant number 200020-188687.

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Funding: C.A.M. acknowledges funding from EPSRC through EP/L015110/1, and C.T. and P.W. through EP/R031924/1. P.W. and T.R. are grateful for support through SARIRF funding by the University of St Andrews. I.M. acknowledges studentship support through the International Max Planck Research School for Chemistry and Physics of Quantum Materials. M.D.W., A.R., and P.D.C.K. acknowledge funding from The Leverhulme Trust. F.M. and P.D.C.K. acknowledge funding from the European Research Council (through the ERC-714193-QUESTDO project). F.M. and P.D.C.K. are grateful for support by the project CALIPSOplus under Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. P.D.C.K. acknowledges support from the UK Royal Society.

•Jan 1, 2021•10 citations
Acknowledgements: AB acknowledges financial support from the European Research Council (ERC Grant Agreement No. 81876) and VILLUM FONDEN via the QMATH Centre of Excellence (Grant No.10059). Moreover, AB is supported by the French National Research Agency in the framework of the “France 2030” program (ANR-11-LABX-0025-01) for the LabEx PERSYVAL. AC acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 470903074 – TRR 352. APH is partially supported by the Escuela Técnica Superior de Ingenieros Industriales (UNED) of Spain, project 2023-ETSII-UNED-01, as well as by the Spanish Ministerio de Ciencia e Innovación project PID2020-113523GB-I00 and by Comunidad de Madrid project QUITEMAD-CM P2018/TCS4342. AC and AB are grateful for the hospitality of Perimeter Institute where part of this work was carried out. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. This research was also supported in part by the Simons Foundation through the Simons Foundation Emmy Noether Fellows Program at Perimeter Institute.
A quantum computer exhibits quantum advantage when it can perform a calculation that a classical computer is unable to complete. It follows that a company with a quantum computer would be a monopolist in the market for such a calculation if its only competitor was a company with a classical computer. Conversely, economic outcomes are unclear if quantum computers do not exhibit a quantum advantage, but classical and quantum computers have different cost structures. We model a Cournot duopoly where a quantum computing company competes against a classical computing company. The model features an asymmetric variable cost structure between the two companies and the potential for an asymmetric fixed cost structure, where each firm can invest in scaling its hardware to expand its respective market. We find that even if (1) the companies can complete identical calculations, and thus there is no quantum advantage, and (2) it is more expensive to scale the quantum computer, the quantum computing company may be more profitable and also invest more in market creation due to efficiency gains from using quantum algorithms. Finally, we provide examples of settings where the classical computer can also perform a calculation, but not in a cost-effective enough manner to be commercially viable. In such a setting, the quantum computing company becomes a monopolist despite exhibiting no quantum advantage. Taken together, quantum computers may not need to display a quantum advantage to be able to generate a quantum economic advantage for the companies that deploy them. This paper was accepted by D. J. Wu, information systems. Funding: R. G. Melko is supported by the Natural Sciences and Engineering Research Council of Canada, Canada Research Chair program, and the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. A. Goldfarb is supported by the Sloan Foundation and the Social Sciences and Humanities Council of Canada. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4578 .
All data for the preprint "Observation of many-body dynamical localization" The Innsbruck team acknowledges funding by a Wittgenstein prize grant under Austrian Science Fund (FWF) project number Z336-N36, by the European Research Council (ERC) under project number 789017, by an FFG infrastructure grant with project number FO999896041, and by the FWF's COE 1 and quantA . MH thanks the doctoral school ALM for hospitality, with funding from the FWF under the project number W1259-N27.The team at Zhejiang University is supported by the National Natural Science Foundation of China (Grant No. 12375021) and the National Key R\&D Program of China (Grant No. 2022YFA1404203).HY is also supported by the Swiss National Science Foundation under grant number 200020-188687.
Funding: C.A.M. acknowledges funding from EPSRC through EP/L015110/1, and C.T. and P.W. through EP/R031924/1. P.W. and T.R. are grateful for support through SARIRF funding by the University of St Andrews. I.M. acknowledges studentship support through the International Max Planck Research School for Chemistry and Physics of Quantum Materials. M.D.W., A.R., and P.D.C.K. acknowledge funding from The Leverhulme Trust. F.M. and P.D.C.K. acknowledge funding from the European Research Council (through the ERC-714193-QUESTDO project). F.M. and P.D.C.K. are grateful for support by the project CALIPSOplus under Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. P.D.C.K. acknowledges support from the UK Royal Society.