Why can a global cost create a barren plateau?

Question: Consider a shallow parameterized quantum circuit acting on n qubits. Which statement best reflects known cost-function-dependent barren-plateau results? A) A global observable can produce exponentially vanishing gradients even for relatively shallow circuits, whereas suitably local costs can have more favorable gradient scaling B) Local observables necessarily produce constant-size gradients independent of circuit depth and system size C) Global observables cause barren plateaus only after the circuit forms an exact unitary 2-design D) Barren plateaus are solely caused by hardware noise and therefore disappear on ideal simulators Correct: A Explanation: The locality of the cost function can strongly affect trainability. Global costs may require coordinating information across the full system and can exhibit exponentially suppressed gradients even at shallow depth, while local costs can avoid this scaling under appropriate depth and circuit assumptions. Topic: advanced quantum computing / variational algorithms / barren plateaus