Commuting quantum circuits with few outputs are unlikely to be classically simulatable

Yasuhiro Takahashi, Seiichiro Tani, Takeshi Yamazaki, Kazuyuki Tanaka

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an exponentially small additive error in classical polynomial time. Our main result is that there exists a commuting quantum circuit that is not classically simulatable unless the polynomial hierarchy collapses to the third level. This is the first formal evidence that a commuting quantum circuit is not classically simulatable even when the number of output qubits is exponentially small. Then, we consider a generalized version of the circuit and clarify the condition under which it is classically simulatable. We apply these results to examining the ability of IQP circuits to implement fundamental operations, and to examining the classical simulatability of slightly extended Clifford circuits.

本文言語English
ホスト出版物のタイトルComputing and Combinatorics - 21st International Conference, COCOON 2015, Proceedings
編集者Dachuan Xu, Donglei Du, Dingzhu Du
出版社Springer Verlag
ページ223-234
ページ数12
ISBN(印刷版)9783319213972
DOI
出版ステータスPublished - 2015
イベント21st International Conference on Computing and Combinatorics Conference, COCOON 2015 - Beijing, China
継続期間: 2015 8 42015 8 6

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)
9198
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other21st International Conference on Computing and Combinatorics Conference, COCOON 2015
国/地域China
CityBeijing
Period15/8/415/8/6

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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