Quantum Approximate Counting, Simplified Article Swipe
Scott Aaronson
,
Patrick Rall
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1137/1.9781611976014.5
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1137/1.9781611976014.5
In 1998, Brassard, Hoyer, Mosca, and Tapp (BHMT) gave a quantum algorithm for\napproximate counting. Given a list of $N$ items, $K$ of them marked, their\nalgorithm estimates $K$ to within relative error $\\varepsilon$ by making only\n$O\\left( \\frac{1}{\\varepsilon}\\sqrt{\\frac{N}{K}}\\right) $ queries. Although\nthis speedup is of "Grover" type, the BHMT algorithm has the curious feature of\nrelying on the Quantum Fourier Transform (QFT), more commonly associated with\nShor's algorithm. Is this necessary? This paper presents a simplified\nalgorithm, which we prove achieves the same query complexity using Grover\niterations only. We also generalize this to a QFT-free algorithm for amplitude\nestimation. Related approaches to approximate counting were sketched previously\nby Grover, Abrams and Williams, Suzuki et al., and Wie (the latter two as we\nwere writing this paper), but in all cases without rigorous analysis.\n
Related Topics
Concepts
Speedup
Quantum
Algorithm
Quantum phase estimation algorithm
Quantum algorithm
Computer science
Fourier transform
Quantum Fourier transform
Feature (linguistics)
Counting problem
Mathematics
Physics
Quantum mechanics
Parallel computing
Quantum gate
Quantum error correction
Mathematical analysis
Linguistics
Philosophy
Metadata
- Type
- book-chapter
- Language
- en
- Landing Page
- https://doi.org/10.1137/1.9781611976014.5
- https://epubs.siam.org/doi/pdf/10.1137/1.9781611976014.5
- OA Status
- bronze
- Cited By
- 104
- References
- 16
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2971322484
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2971322484Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1137/1.9781611976014.5Digital Object Identifier
- Title
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Quantum Approximate Counting, SimplifiedWork title
- Type
-
book-chapterOpenAlex work type
- Language
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enPrimary language
- Publication year
-
2019Year of publication
- Publication date
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2019-12-17Full publication date if available
- Authors
-
Scott Aaronson, Patrick RallList of authors in order
- Landing page
-
https://doi.org/10.1137/1.9781611976014.5Publisher landing page
- PDF URL
-
https://epubs.siam.org/doi/pdf/10.1137/1.9781611976014.5Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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bronzeOpen access status per OpenAlex
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https://epubs.siam.org/doi/pdf/10.1137/1.9781611976014.5Direct OA link when available
- Concepts
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Speedup, Quantum, Algorithm, Quantum phase estimation algorithm, Quantum algorithm, Computer science, Fourier transform, Quantum Fourier transform, Feature (linguistics), Counting problem, Mathematics, Physics, Quantum mechanics, Parallel computing, Quantum gate, Quantum error correction, Mathematical analysis, Linguistics, PhilosophyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
104Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 5, 2024: 21, 2023: 25, 2022: 25, 2021: 18Per-year citation counts (last 5 years)
- References (count)
-
16Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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