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: https://drops.dagstuhl.de/opus/volltexte/2021/14004/
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van Apeldoorn, Joran

Quantum Probability Oracles & Multidimensional Amplitude Estimation

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LIPIcs-TQC-2021-9.pdf (0.7 MB)


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 𝓁₁-norm (the total variation distance) estimation and a Õ(√n/ε) query algorithm for 𝓁₂-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}
}

Keywords: quantum algorithms, amplitude estimation, monte carlo
Collection: 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)
Issue Date: 2021
Date of publication: 22.06.2021


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