Hardness of classically simulating quantum circuits with unbounded Toffoli and fan-out gates

Yasuhiro Takahashi, Takeshi Yamazaki, Kazuyuki Tanaka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the classical simulatability of constant-depth quantum circuits followed by only one single-qubit measurement, where they consist of universal gates on at most two qubits and additional gates on an unbounded number of qubits. First, we consider unbounded Toffoli gates as additional gates and deal with the weak simulation, i.e., sampling the output probability distribution. We show that there exists a constant-depth quantum circuit with only one unbounded Toffoli gate that is not weakly simulatable, unless BQP ⊆ PostBPP ∩ AM. Then, we consider unbounded fan-out gates as additional gates and deal with the strong simulation, i.e., computing the output probability. We show that there exists a constant-depth quantum circuit with only two unbounded fan-out gates that is not strongly simulatable, unless P = PP. These results are in contrast to the fact that any constant-depth quantum circuit without additional gates is strongly and weakly simulatable.

Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings
Pages801-812
Number of pages12
DOIs
Publication statusPublished - 2013 Oct 15
Event38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 - Klosterneuburg, Austria
Duration: 2013 Aug 262013 Aug 30

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8087 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013
CountryAustria
CityKlosterneuburg
Period13/8/2613/8/30

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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