Quantum advantage for differential equation analysis
Name
PhysRevA.105.022415.pdf
Size
1.37 MB
Format
Adobe PDF
Checksum (MD5)
37410d79e92752ad3ffab747f40a7305
Author(s)
Kiani, Bobak Toussi
De Palma, Giacomo
Englund, Dirk
Kaminsky, William
Marvian, Milad
Lloyd, Seth
Date Issued
February 14, 2022
Journal
Physical Review A
Publisher
American Physical Society
Citation
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).
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
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.
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DOI of Published Version
https://doi.org/10.1103/physreva.105.022415
