Quantum advantage for differential equation analysis
Quantum algorithms for differential equation solving, data processing, and machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in useful problem instances. The essential obstacle for qu...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2024
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| Online Access: | https://hdl.handle.net/1721.1/153943 |
| _version_ | 1811068413462708224 |
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| author | Kiani, Bobak Toussi De Palma, Giacomo Englund, Dirk Kaminsky, William Marvian, Milad Lloyd, Seth |
| author_facet | Kiani, Bobak Toussi De Palma, Giacomo Englund, Dirk Kaminsky, William Marvian, Milad Lloyd, Seth |
| author_sort | Kiani, Bobak Toussi |
| collection | MIT |
| description | Quantum algorithms for differential equation solving, data processing, and machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in useful problem instances. The essential obstacle for quantum differential equation solving is that outputting useful information may require difficult postprocessing, and the essential obstacle for quantum data processing and machine learning is that inputting the data is a difficult task just by itself. In this study, we demonstrate that, when combined, these difficulties solve one another. We show how the output of quantum differential equation solving can serve as the input for quantum data processing and machine learning, allowing dynamical analysis in terms of principal components, power spectra, and wavelet decompositions. To illustrate this, we consider continuous-time Markov processes on epidemiological and social networks. These quantum algorithms provide an exponential advantage over existing classical Monte Carlo methods. |
| first_indexed | 2024-09-23T07:55:38Z |
| format | Article |
| id | mit-1721.1/153943 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T07:55:38Z |
| publishDate | 2024 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1539432024-04-20T07:23:11Z Quantum advantage for differential equation analysis Kiani, Bobak Toussi De Palma, Giacomo Englund, Dirk Kaminsky, William Marvian, Milad Lloyd, Seth Quantum algorithms for differential equation solving, data processing, and machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in useful problem instances. The essential obstacle for quantum differential equation solving is that outputting useful information may require difficult postprocessing, and the essential obstacle for quantum data processing and machine learning is that inputting the data is a difficult task just by itself. In this study, we demonstrate that, when combined, these difficulties solve one another. We show how the output of quantum differential equation solving can serve as the input for quantum data processing and machine learning, allowing dynamical analysis in terms of principal components, power spectra, and wavelet decompositions. To illustrate this, we consider continuous-time Markov processes on epidemiological and social networks. These quantum algorithms provide an exponential advantage over existing classical Monte Carlo methods. 2024-03-26T19:34:12Z 2024-03-26T19:34:12Z 2022-02-14 2024-03-26T19:20:46Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 https://hdl.handle.net/1721.1/153943 Kiani, Bobak Toussi, De Palma, Giacomo, Englund, Dirk, Kaminsky, William, Marvian, Milad et al. 2022. "Quantum advantage for differential equation analysis." Physical Review A, 105 (2). en 10.1103/physreva.105.022415 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society American Physical Society |
| spellingShingle | Kiani, Bobak Toussi De Palma, Giacomo Englund, Dirk Kaminsky, William Marvian, Milad Lloyd, Seth Quantum advantage for differential equation analysis |
| title | Quantum advantage for differential equation analysis |
| title_full | Quantum advantage for differential equation analysis |
| title_fullStr | Quantum advantage for differential equation analysis |
| title_full_unstemmed | Quantum advantage for differential equation analysis |
| title_short | Quantum advantage for differential equation analysis |
| title_sort | quantum advantage for differential equation analysis |
| url | https://hdl.handle.net/1721.1/153943 |
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