Efficient State Preparation for Quantum Amplitude Estimation

Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If preparation too expensive, it diminish the quantum advantage. Preparing arbitrary states has exponential complexity with respect number of qubits, thus, not applicable. Currently known techniques require problems based on log-concave probability distributions, involve learning an unknown distribution from empirical data, or fully rely arithmetic. In paper, we introduce approach simplify preparation, together circuit optimization technique, both which help reduce QAE significantly. We demonstrate introduced numerical integration example real hardware, as well option pricing under Heston model, i.e., stochastic volatility process, using