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Classical Simulation Complexity of Quantum Branching Programs

Authors: Farid Ablayev

Published in: Dagstuhl Seminar Proceedings, Volume 7411, Algebraic Methods in Computational Complexity (2008)

Abstract

We present classical simulation techniques for measure once quantum branching programs. For bounded error syntactic quantum branching program of width $w$ that computes a function with error $delta$ we present a classical deterministic branching program of the same length and width at most $(1+2/(1-2delta))^{2w}$ that computes the same function. Second technique is a classical stochastic simulation technique for bounded error and unbounded error quantum branching programs. Our result is that it is possible stochastically-classically simulate quantum branching programs with the same length and almost the same width, but we lost bounded error acceptance property.

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Farid Ablayev. Classical Simulation Complexity of Quantum Branching Programs. In Algebraic Methods in Computational Complexity. Dagstuhl Seminar Proceedings, Volume 7411, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{ablayev:DagSemProc.07411.3,
  author =	{Ablayev, Farid},
  title =	{{Classical Simulation Complexity of  Quantum  Branching Programs}},
  booktitle =	{Algebraic Methods in Computational Complexity},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7411},
  editor =	{Manindra Agrawal and Harry Buhrman and Lance Fortnow and Thomas Thierauf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07411.3},
  URN =		{urn:nbn:de:0030-drops-13107},
  doi =		{10.4230/DagSemProc.07411.3},
  annote =	{Keywords: Quantum algorithms, Branching Programs, Complexity}
}

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Classical Simulation Complexity of Quantum Branching Programs

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