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.2023.10
URN: urn:nbn:de:0030-drops-183206
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18320/
Kretschmer, William
Quantum Mass Production Theorems
Abstract
We prove that for any n-qubit unitary transformation U and for any r = 2^{o(n / log n)}, there exists a quantum circuit to implement U^{⊗ r} with at most O(4ⁿ) gates. This asymptotically equals the number of gates needed to implement just a single copy of a worst-case U. We also establish analogous results for quantum states and diagonal unitary transformations. Our techniques are based on the work of Uhlig [Math. Notes 1974], who proved a similar mass production theorem for Boolean functions.
BibTeX - Entry
@InProceedings{kretschmer:LIPIcs.TQC.2023.10,
author = {Kretschmer, William},
title = {{Quantum Mass Production Theorems}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {10:1--10:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-283-9},
ISSN = {1868-8969},
year = {2023},
volume = {266},
editor = {Fawzi, Omar and Walter, Michael},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18320},
URN = {urn:nbn:de:0030-drops-183206},
doi = {10.4230/LIPIcs.TQC.2023.10},
annote = {Keywords: mass production, quantum circuit synthesis, quantum circuit complexity}
}
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Keywords: |
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mass production, quantum circuit synthesis, quantum circuit complexity |
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Collection: |
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18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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18.07.2023 |
