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Quantum Algorithm for Data Fitting

Author(s)
Wiebe, Nathan; Braun, Daniel; Lloyd, Seth
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Abstract
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently [Harrow et al., Phys. Rev. Lett. 103 150502 (2009)]. In many cases, our algorithm can also efficiently find a concise function that approximates the data to be fitted and bound the approximation error. In cases where the input data are pure quantum states, the algorithm can be used to provide an efficient parametric estimation of the quantum state and therefore can be applied as an alternative to full quantum-state tomography given a fault tolerant quantum computer.
Date issued
2012-08
URI
http://hdl.handle.net/1721.1/73873
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Wiebe, Nathan, Daniel Braun, and Seth Lloyd. “Quantum Algorithm for Data Fitting.” Physical Review Letters 109.5 (2012). © 2012 American Physical Society
Version: Final published version
ISSN
0031-9007
1079-7114

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