Verification of hypergraph states

Tomoyuki Morimae, Yuki Takeuchi, and Masahito Hayashi
Phys. Rev. A 96, 062321 – Published 20 December 2017

Abstract

Hypergraph states are generalizations of graph states where controlled-Z gates on edges are replaced with generalized controlled-Z gates on hyperedges. Hypergraph states have several advantages over graph states. For example, certain hypergraph states, such as the Union Jack states, are universal resource states for measurement-based quantum computing with only Pauli measurements, while graph state measurement-based quantum computing needs non-Clifford basis measurements. Furthermore, it is impossible to classically efficiently sample measurement results on hypergraph states unless the polynomial hierarchy collapses to the third level. Although several protocols have been proposed to verify graph states with only sequential single-qubit Pauli measurements, there was no verification method for hypergraph states. In this paper, we propose a method for verifying a certain class of hypergraph states with only sequential single-qubit Pauli measurements. Importantly, no i.i.d. property of samples is assumed in our protocol: any artificial entanglement among samples cannot fool the verifier. As applications of our protocol, we consider verified blind quantum computing with hypergraph states, and quantum computational supremacy demonstrations with hypergraph states.

  • Figure
  • Received 28 February 2017

DOI:https://doi.org/10.1103/PhysRevA.96.062321

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Quantum Information, Science & Technology

Authors & Affiliations

Tomoyuki Morimae1,2,*, Yuki Takeuchi3,†, and Masahito Hayashi4,5,‡

  • 1Department of Computer Science, Gunma University, 1-5-1 Tenjincho Kiryushi Gunma, 376-0052, Japan
  • 2JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
  • 3Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
  • 4Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
  • 5Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117542, Singapore

  • *morimae@gunma-u.ac.jp
  • takeuchi@qi.mp.es.osaka-u.ac.jp
  • masahito@math.nagoya-u.ac.jp

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Issue

Vol. 96, Iss. 6 — December 2017

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