Energy Risk Analysis With Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling

In this article, we generalize the approximate quantum compiling algorithm into a new method for <sc>cnot</sc>-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 ten-qubit experimental demonstration of iterative amplitude estimation on a quantum computer. The target application is a 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&#x2013;classical iterations (again in the order of the binary precision) compared to the iterative amplitude estimation. The calculation of the expected value, value at risk, and conditional value at risk of contract portfolios on quantum hardware provides a proof of principle of the new algorithm.