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

Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling