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Graph states and cluster states play critical roles in quantum computing. Graph states are a class of multi-qubit entangled states formed by applying controlled-Z gates to n qubits initialized in the |+⟩ state. They use mathematical graphs to intuitively represent multi-qubit entanglement relationships, where the graph structure uniquely defines a specific graph state.
Cluster states, a subset of graph states, typically exhibit chain or lattice structures. Their key property is the existence of direct or indirect entanglement between any two qubits, making them the fundamental resource for MBQC by enabling global quantum computation through local measurements. |