License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2021.9
URN: urn:nbn:de:0030-drops-140046
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14004/
van Apeldoorn, Joran
Quantum Probability Oracles & Multidimensional Amplitude Estimation
Abstract
We give a multidimensional version of amplitude estimation. Let p be an n-dimensional probability distribution which can be sampled from using a quantum circuit U_p. We show that all coordinates of p can be estimated up to error ε per coordinate using Õ(1/(ε)) applications of U_p and its inverse. This generalizes the normal amplitude estimation algorithm, which solves the problem for n = 2. Our results also imply a Õ(n/ε) query algorithm for ?₁-norm (the total variation distance) estimation and a Õ(√n/ε) query algorithm for ?₂-norm. We also show that these results are optimal up to logarithmic factors.
BibTeX - Entry
@InProceedings{vanapeldoorn:LIPIcs.TQC.2021.9,
author = {van Apeldoorn, Joran},
title = {{Quantum Probability Oracles \& Multidimensional Amplitude Estimation}},
booktitle = {16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
pages = {9:1--9:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-198-6},
ISSN = {1868-8969},
year = {2021},
volume = {197},
editor = {Hsieh, Min-Hsiu},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14004},
URN = {urn:nbn:de:0030-drops-140046},
doi = {10.4230/LIPIcs.TQC.2021.9},
annote = {Keywords: quantum algorithms, amplitude estimation, monte carlo}
}
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Keywords: |
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quantum algorithms, amplitude estimation, monte carlo |
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Collection: |
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16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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22.06.2021 |
