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Parallel Quantum Computation and Quantum Codes

Authors:

Cristopher Moore,

Martin NilssonAuthors Info & Claims

SIAM Journal on Computing, Volume 31, Issue 3

Pages 799 - 815

https://doi.org/10.1137/S0097539799355053

Published: 01 March 2002 Publication History

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Abstract

We study the class QNC of efficient parallel quantum circuits, the quantum analog of NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or, more generally, any circuit consisting of controlled-not gates, controlled $\pi$-shifts, and Hadamard gates. Finally, while we note the exact quantum Fourier transform can be parallelized to linear depth, we conjecture that neither it nor a simpler "staircase" circuit can be parallelized to less than this.

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Girish USinha MTal AWu KMohar BShinkar IO'Donnell R(2024)The Power of Adaptivity in Quantum Query AlgorithmsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649621(1488-1497)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649621
Lai CCheng H(2022)Learning quantum circuits of T -depth one2022 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT50566.2022.9834452(2213-2218)Online publication date: 26-Jun-2022
https://dl.acm.org/doi/10.1109/ISIT50566.2022.9834452
Grier DSchaeffer LMakarychev KMakarychev YTulsiani MKamath GChuzhoy J(2020)Interactive shallow Clifford circuits: Quantum advantage against NC¹ and beyondProceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3357713.3384332(875-888)Online publication date: 22-Jun-2020
https://dl.acm.org/doi/10.1145/3357713.3384332
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Parallel Quantum Computation and Quantum Codes

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Published In

SIAM Journal on Computing Volume 31, Issue 3

2001

324 pages

ISSN:0097-5397

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Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 March 2002

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Girish USinha MTal AWu KMohar BShinkar IO'Donnell R(2024)The Power of Adaptivity in Quantum Query AlgorithmsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649621(1488-1497)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649621
Lai CCheng H(2022)Learning quantum circuits of T -depth one2022 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT50566.2022.9834452(2213-2218)Online publication date: 26-Jun-2022
https://dl.acm.org/doi/10.1109/ISIT50566.2022.9834452
Grier DSchaeffer LMakarychev KMakarychev YTulsiani MKamath GChuzhoy J(2020)Interactive shallow Clifford circuits: Quantum advantage against NC¹ and beyondProceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3357713.3384332(875-888)Online publication date: 22-Jun-2020
https://dl.acm.org/doi/10.1145/3357713.3384332
Watts AKothari RSchaeffer LTal ACharikar MCohen E(2019)Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuitsProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316404(515-526)Online publication date: 23-Jun-2019
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Jeffery SMagniez FWolf R(2017)Optimal Parallel Quantum Query AlgorithmsAlgorithmica10.1007/s00453-016-0206-z79:2(509-529)Online publication date: 1-Oct-2017
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Takahashi YTani S(2016)Collapse of the Hierarchy of Constant-Depth Exact Quantum CircuitsComputational Complexity10.1007/s00037-016-0140-025:4(849-881)Online publication date: 1-Dec-2016
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Gottesman D(2014)Fault-tolerant quantum computation with constant overheadQuantum Information & Computation10.5555/2685179.268518414:15-16(1338-1372)Online publication date: 1-Nov-2014
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Takahashi YYamazaki TTanaka K(2014)Hardness of classically simulating quantum circuits with unbounded Toffoli and fan-out gatesQuantum Information & Computation10.5555/2685164.268517114:13-14(1149-1164)Online publication date: 1-Oct-2014
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García HMarkov ICross A(2014)On the geometry of stabilizer statesQuantum Information & Computation10.5555/2638682.263869114:7&8(683-720)Online publication date: 1-May-2014
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Maynard CPius E(2014)A quantum multiply-accumulatorQuantum Information Processing10.1007/s11128-013-0715-513:5(1127-1138)Online publication date: 1-May-2014
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