Robust Verification of Graph States Under Adversarial Scenario and Noisy Measurements
Qingshan Xu, Xiaoqing Tan, Zhipeng Xiao, Daipengwei Bao, Qin Li, Rui Huang · Advanced Quantum Technologies · 2025
Abstract Graph states are resource states for measurement‐based quantum computation. Verification of graph states aims to certify whether a quantum state prepared by an untrusted device is close to an ideal graph state or not. Existing verification methods have not considered verifying graph states under an adversarial scenario and noisy measurements. In this paper, a robust verification method for graph states is proposed to overcome this issue. First, a verification model for graph states is designed. Then, two types of verification protocols based on this model are proposed. In addition, the completeness and soundness of the verification protocols are calculated when the measurement devices are affected by noises. Afterward, the measurement strategy of the robust verification protocols is extended from the specific case to the general case. In order to obtain the soundness that scales as , the verification method only requires copies of the graph state, where is the size of the graph state. Finally, several numerical examples are presented to demonstrate the effect of noises on the completeness and soundness of the verification protocols.