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arXiv · 1701.05688

Verified measurement-based quantum computing with hypergraph states

Tomoyuki Morimae·Yuki Takeuchi·Masahito Hayashi
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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 with a constant $L$1-norm error 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 hypergraph states with only sequential single-qubit Pauli measurements. As applications, we consider verified blind quantum computing with hypergraph states, and quantum supremacy demonstrations with hypergraph states.

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Tomoyuki Morimae, Yuki Takeuchi, Masahito Hayashi. 2017-01-20. Verified measurement-based quantum computing with hypergraph states. https://doi.org/10.1103/physreva.96.062321

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