  We generalize the Approximate Quantum Compiling algorithm into a new method
for CNOT-depth reduction, which is apt to process wide target quantum circuits.
Combining this method with state-of-the-art techniques for error mitigation and
circuit compiling, we present a 10-qubit experimental demonstration of
Iterative Amplitude Estimation on a quantum computer. The target application is
the derivation of the Expected Value of contract portfolios in the energy
industry. In parallel, we also introduce a new variant of the Quantum Amplitude
Estimation algorithm which we call Dynamic Amplitude Estimation, as it is based
on the dynamic circuit capability of quantum devices. The algorithm achieves a
reduction in the circuit width in the order of the binary precision compared to
the typical implementation of Quantum Amplitude Estimation, while
simultaneously decreasing the number of quantum-classical iterations (again in
the order of the binary precision) compared to the Iterative Amplitude
Estimation. The calculation of the Expected Value, VaR and CVaR of contract
portfolios on quantum hardware provides a proof of principle of the new
algorithm.
