2 Search Results for "Tamate, Shuhei"

Document
DOI: 10.4230/LIPIcs.CCC.2025.5
Improved Separation Between Quantum and Classical Computers for Sampling and Functional Tasks

Authors: Simon C. Marshall, Scott Aaronson, and Vedran Dunjko

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with postselection are as powerful as classical computers with postselection (PostBQP = PostBPP), (ii) any one of several quantum sampling experiments (BosonSampling, IQP, DQC1) can be approximately performed by a classical computer (contingent on existing assumptions). This last result implies that if any of these experiment’s hardness conjectures hold, then quantum computers can implement functions classical computers cannot (FBQP≠ FBPP) unless the polynomial hierarchy collapses to its 2nd level. These results are an improvement over previous work which either achieved a collapse to the third level or were concerned with exact sampling, a physically impractical case. The workhorse of these results is a new technical complexity-theoretic result which we believe could have value beyond quantum computation. In particular, we prove that if there exists an equivalence between problems solvable with an exact counting oracle and problems solvable with an approximate counting oracle, then the polynomial hierarchy collapses to its second level, indeed to ZPP^NP.
Cite as

Simon C. Marshall, Scott Aaronson, and Vedran Dunjko. Improved Separation Between Quantum and Classical Computers for Sampling and Functional Tasks. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{marshall_et_al:LIPIcs.CCC.2025.5,
  author =	{Marshall, Simon C. and Aaronson, Scott and Dunjko, Vedran},
  title =	{{Improved Separation Between Quantum and Classical Computers for Sampling and Functional Tasks}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.5},
  URN =		{urn:nbn:de:0030-drops-236991},
  doi =		{10.4230/LIPIcs.CCC.2025.5},
  annote =	{Keywords: Quantum advantage, Approximate counting, Boson sampling}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.13
Power of Quantum Computation with Few Clean Qubits

Authors: Keisuke Fujii, Hirotada Kobayashi, Tomoyuki Morimae, Harumichi Nishimura, Shuhei Tamate, and Seiichiro Tani

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No initializations of qubits are allowed during the computation, nor are intermediate measurements. The main contribution of this paper is to develop unexpectedly strong error-reduction methods for such quantum computations that simultaneously reduce the number of necessary clean qubits. It is proved that any problem solvable by a polynomialtime quantum computation with one-sided bounded error that uses logarithmically many clean qubits is also solvable with exponentially small one-sided error using just two clean qubits, and with polynomially small one-sided error using just one clean qubit. It is further proved in the twosided-error case that any problem solvable by such a computation with a constant gap between completeness and soundness using logarithmically many clean qubits is also solvable with exponentially small two-sided error using just two clean qubits. If only one clean qubit is available, the problem is again still solvable with exponentially small error in one of the completeness and soundness and with polynomially small error in the other. An immediate consequence is that the Trace Estimation problem defined with fixed constant threshold parameters is complete for BQ_{[1]}P and BQ_{log}P, the classes of problems solvable by polynomial-time quantum computations with completeness 2/3 and soundness 1/3 using just one and logarithmically many clean qubits, respectively. The techniques used for proving the error-reduction results may be of independent interest in themselves, and one of the technical tools can also be used to show the hardness of weak classical simulations of one-clean-qubit computations (i.e., DQC1 computations).
Cite as

Keisuke Fujii, Hirotada Kobayashi, Tomoyuki Morimae, Harumichi Nishimura, Shuhei Tamate, and Seiichiro Tani. Power of Quantum Computation with Few Clean Qubits. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fujii_et_al:LIPIcs.ICALP.2016.13,
  author =	{Fujii, Keisuke and Kobayashi, Hirotada and Morimae, Tomoyuki and Nishimura, Harumichi and Tamate, Shuhei and Tani, Seiichiro},
  title =	{{Power of Quantum Computation with Few Clean Qubits}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.13},
  URN =		{urn:nbn:de:0030-drops-62960},
  doi =		{10.4230/LIPIcs.ICALP.2016.13},
  annote =	{Keywords: DQC1, quantum computing, complete problems, error reduction}
}
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