For QAOA with a real mixer and a diagonal cost Hamiltonian, a nonzero final-mixer-angle gradient requires nonzero imaginary coherence between mixer-connected basis states, yielding an exact bound in terms of imaginarity.
Hillery, Coherence as a resource in decision problems: The Deutsch–Jozsa algorithm and a variation, Phys
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Imaginarity as a necessary resource for trainability in QAOA
For QAOA with a real mixer and a diagonal cost Hamiltonian, a nonzero final-mixer-angle gradient requires nonzero imaginary coherence between mixer-connected basis states, yielding an exact bound in terms of imaginarity.