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