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its eigenvalues satisfy The mixing Hamiltonian H_M depends on D and its structure and is in the unconstrained case (i.e. when D={0,1}^n) usually taken to be the transverse field Hamiltonian H_M=∑_j X_j. Constraints (i.e. when D⊂{0,1}^n) can be incorporated directly into the mixing Hamiltonian or