# Verified measurement-based quantum computing with hypergraph states

## TL;DR

This paper introduces a verification method for hypergraph states using only sequential single-qubit Pauli measurements, enabling secure blind quantum computing and quantum supremacy demonstrations.

## Contribution

It presents the first verification protocol for hypergraph states, expanding measurement-based quantum computing capabilities.

## Key findings

- Hypergraph states can be verified with simple measurements.
- Hypergraph states enable universal measurement-based quantum computing.
- Verification supports secure blind quantum computing and quantum supremacy.

## 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.