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.ISAAC.2022.6
URN: urn:nbn:de:0030-drops-172918
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17291/
Go to the corresponding LIPIcs Volume Portal

Hasegawa, Atsuya ; Le Gall, François

An Optimal Oracle Separation of Classical and Quantum Hybrid Schemes

pdf-format:
LIPIcs-ISAAC-2022-6.pdf (1 MB)

Abstract

Recently, Chia, Chung and Lai (STOC 2020) and Coudron and Menda (STOC 2020) have shown that there exists an oracle ? such that BQP^? ≠ (BPP^BQNC)^? ∪ (BQNC^BPP)^?. In fact, Chia et al. proved a stronger statement: for any depth parameter d, there exists an oracle that separates quantum depth d and 2d+1, when polynomial-time classical computation is allowed. This implies that relative to an oracle, doubling quantum depth gives classical and quantum hybrid schemes more computational power.
In this paper, we show that for any depth parameter d, there exists an oracle that separates quantum depth d and d+1, when polynomial-time classical computation is allowed. This gives an optimal oracle separation of classical and quantum hybrid schemes. To prove our result, we consider d-Bijective Shuffling Simon’s Problem (which is a variant of d-Shuffling Simon’s Problem considered by Chia et al.) and an oracle inspired by an "in-place" permutation oracle.

BibTeX - Entry

@InProceedings{hasegawa_et_al:LIPIcs.ISAAC.2022.6,
  author =	{Hasegawa, Atsuya and Le Gall, Fran\c{c}ois},
  title =	{{An Optimal Oracle Separation of Classical and Quantum Hybrid Schemes}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17291},
  URN =		{urn:nbn:de:0030-drops-172918},
  doi =		{10.4230/LIPIcs.ISAAC.2022.6},
  annote =	{Keywords: small-depth quantum circuit, hybrid quantum computer, oracle separation}
}

Keywords: small-depth quantum circuit, hybrid quantum computer, oracle separation
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI