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

Yasuhiro Takahashi, Takeshi Yamazaki, Kazuyuki Tanaka

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトルMathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings
ページ801-812
ページ数12
DOI
出版ステータスPublished - 2013
イベント38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 - Klosterneuburg, Austria
継続期間: 2013 8 262013 8 30

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
8087 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

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

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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