Quantum Fourier Iterative Amplitude Estimation

by Jorge Juan Martinez De Lejarza Samper (IFIC-Universitat de València)

Thursday 28 Sept 2023, 10:00 → 11:00 Europe/Zurich

4/2-037 - TH meeting room (CERN)

Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several algorithms have been proposed to achieve this goal. In this talk, I will present an application of Quantum Machine Learning (QML) and Grover's amplification algorithm to build a new tool for estimating Monte Carlo integrals. Our method, Quantum Fourier Iterative Amplitude Estimation (QFIAE), decomposes the target function into its Fourier series using a Quantum Neural Network (QNN), and then integrates each trigonometric component using Iterative Quantum Amplitude Estimation (IQAE). This approach builds on Fourier Quantum Monte Carlo Integration (FQMCI), but QFIAE avoids the need for numerical integration of Fourier coefficients. This approach reduces the computational load while maintaining the quadratic speedup achieved by IQAE. To evaluate the performance of QFIAE, we apply it to a particle physics scattering process and compare its accuracy with other quantum integration methods and the analytic result. Our results show that QFIAE achieves comparable accuracy while being suitable for execution on real hardware.

QFIAE_QTI-TH_FORUM_Martinez_de_Lejarza.pdf