Efficient verification of two-colorable graph states

Graph states known as the resource states for measurement-based quantum computation play an important role in quantum information processing. Verifying the correctness of graph states in an efficient way is crucial to scalable quantum computing. In this paper, we propose an efficient method for verifying two-colorable graph states with Pauli measurements, where the number of required measurement settings is a constant that is independent of the size of graph states. In addition, the number of required tests is less than the existing protocols. We also present several examples, such as the brickwork state and the two-dimensional square lattice state, to show how to get the specific verification strategy. Furthermore, we propose a robust verification of graph states for resisting the noise acting on the measurement device. Finally, based on the verification of two-colorable graph states in the adversarial scenario, we propose a verifiable blind quantum computing protocol, which can realize the less resource overhead.