The Significance of the Quantum Volume for Other Algorithms: A Case Study for Quantum Amplitude Estimation

The quantum volume is a comprehensive, single number metric to describe the computational power of a quantum computer. It has grown exponentially in the recent past. In this study we will assume this remains the case and translate this development into the performance development of another quantum algorithms, quantum amplitude estimation. This is done using a noise model that estimates the error probability of a single run of an algorithm. Its parameters are related to the quantum volume under the model’s assumptions. Applying the same noise model to quantum amplitude estimation, it is possible to relate the error rate to the generated Fisher information per second, which is the main performance metric of quantum amplitude estimation as a numerical integration technique. This provides a prediction of its integration capabilities and shows that quantum amplitude estimation as a numerical integration technique will not provide an advantage over classical alternatives in the near future without major breakthroughs.