License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.MFCS.2022.81
URN: urn:nbn:de:0030-drops-168798
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16879/
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Tani, Seiichiro

Space-Bounded Unitary Quantum Computation with Postselection

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LIPIcs-MFCS-2022-81.pdf (0.8 MB)

Abstract

Space-bounded computation has been a central topic in classical and quantum complexity theory. In the quantum case, every elementary gate must be unitary. This restriction makes it unclear whether the power of space-bounded computation changes by allowing intermediate measurement. In the bounded error case, Fefferman and Remscrim [STOC 2021, pp.1343-1356] and Girish, Raz and Zhan [ICALP 2021, pp.73:1-73:20] recently provided the break-through results that the power does not change. This paper shows that a similar result holds for space-bounded quantum computation with postselection. Namely, it is proved possible to eliminate intermediate postselections and measurements in the space-bounded quantum computation in the bounded-error setting. Our result strengthens the recent result by Le Gall, Nishimura and Yakaryilmaz [TQC 2021, pp.10:1-10:17] that logarithmic-space bounded-error quantum computation with intermediate postselections and measurements is equivalent in computational power to logarithmic-space unbounded-error probabilistic computation. As an application, it is shown that bounded-error space-bounded one-clean qubit computation (DQC1) with postselection is equivalent in computational power to unbounded-error space-bounded probabilistic computation, and the computational supremacy of the bounded-error space-bounded DQC1 is interpreted in complexity-theoretic terms.

BibTeX - Entry

@InProceedings{tani:LIPIcs.MFCS.2022.81,
  author =	{Tani, Seiichiro},
  title =	{{Space-Bounded Unitary Quantum Computation with Postselection}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{81:1--81:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16879},
  URN =		{urn:nbn:de:0030-drops-168798},
  doi =		{10.4230/LIPIcs.MFCS.2022.81},
  annote =	{Keywords: quantum complexity theory, space-bounded computation, postselection}
}

Keywords: quantum complexity theory, space-bounded computation, postselection
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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