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

Yasuhiro Takahashi, Seiichiro Tani, Takeshi Yamazaki, Kazuyuki Tanaka

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

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 21st International Conference, COCOON 2015, Proceedings
EditorsDachuan Xu, Donglei Du, Dingzhu Du
PublisherSpringer Verlag
Pages223-234
Number of pages12
ISBN (Print)9783319213972
DOIs
Publication statusPublished - 2015
Event21st International Conference on Computing and Combinatorics Conference, COCOON 2015 - Beijing, China
Duration: 2015 Aug 42015 Aug 6

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9198
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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