Efficient Verification of Hypergraph States

Abstract

Graph states and hypergraph states are of wide interest in quantum information processing and foundational studies. Efficient verification of these states is a key to various applications. Here we propose a simple method for verifying hypergraph states which requires only two distinct Pauli measurements for each party, yet its efficiency is comparable to the best strategy based on entangling measurements. For a given state, the overhead is bounded by the chromatic number and degree of the underlying hypergraph. Our protocol is dramatically more efficient than all previous protocols based on local measurements, including tomography and direct fidelity estimation. It enables the verification of hypergraph states and genuine multipartite entanglement of thousands of qubits. The protocol can also be generalized to the adversarial scenario, while achieving almost the same efficiency. This merit is particularly appealing to demonstrating blind measurement-based quantum computation and quantum supremacy.

10+11 pages, 3 figures, and 1 table; published in Phys. Rev. Applied

References in corpus (12)

• Entanglement detection
• Direct Fidelity Estimation from Few Pauli Measurements
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Entanglement Detection in the Stabilizer Formalism
• Bell Inequalities for Graph States
• Experimental Verification of Multipartite Entanglement in Quantum Networks
• Optimal verification of entangled states with local measurements
• Verification of Many-Qubit States
• Encoding Hypergraphs into Quantum States
• Resource-efficient verification of quantum computing using Serfling's bound
• Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states
• Local unitary symmetries of hypergraph states

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