Where does amplitude estimation obtain its quadratic advantage?

Question: In the ideal query model, how does canonical quantum amplitude estimation compare with classical Monte Carlo estimation for additive error ε? A) Both generally require O(1/ε²) oracle calls, but quantum amplitude estimation uses fewer qubits B) Quantum amplitude estimation can achieve O(1/ε) query scaling, compared with the classical sampling scaling O(1/ε²) C) Quantum amplitude estimation uses O(log(1/ε)) queries because the phase is stored in binary D) Quantum amplitude estimation achieves O(1) query complexity whenever the target probability is nonzero Correct: B Explanation: Classical sampling typically needs a number of independent samples proportional to 1/ε² to estimate a probability to additive precision ε. Ideal amplitude estimation uses coherent applications of the relevant operator to obtain a quadratic improvement to scaling proportional to 1/ε. Topic: advanced quantum computing / amplitude estimation / complexity