Completeness of the classical 2D Ising model and universal quantum computation

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Graph states are usually defined as the joint eigenstates of the operators K j = X j ​ ⨂ k | ( j , k ) ∈ E Z k K_{j}=X_{j}\bigotimes_{k|(j,k)\in E}Z_{k} [ 10 ] . To be precise, | φ G ~ ⟩ |\varphi_{\tilde{G}}\rangle is equivalent to a graph state up to local Hadamard operations on all qubits in V E V_{E}

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