Loop Feynman integration on a quantum computer

TL;DR

This paper presents a new quantum Monte Carlo integrator, QFIAE, that uses a Quantum Neural Network to efficiently evaluate loop Feynman integrals on quantum hardware, demonstrating promising results for one-loop diagrams.

Contribution

Introduction of QFIAE, a quantum Monte Carlo integrator utilizing a Quantum Neural Network for efficient Fourier decomposition of integrands in loop Feynman integrals.

Findings

Successful implementation on a real quantum computer for a one-loop tadpole diagram.

Quantum simulator analysis of more complex one-loop diagrams.

Method shows potential for applications beyond physics, such as finance and AI.

Abstract

This work investigates in detail the performance and advantages of a new quantum Monte Carlo integrator, dubbed Quantum Fourier Iterative Amplitude Estimation (QFIAE), to numerically evaluate for the first time loop Feynman integrals in a near-term quantum computer and a quantum simulator. In order to achieve a quadratic speedup, QFIAE introduces a Quantum Neural Network (QNN) that efficiently decomposes the multidimensional integrand into its Fourier series. For a one-loop tadpole Feynman diagram, we have successfully implemented the quantum algorithm on a real quantum computer and obtained a reasonable agreement with the analytical values. One-loop Feynman diagrams with more external legs have been analyzed in a quantum simulator. These results thoroughly illustrate how our quantum algorithm effectively estimates loop Feynman integrals and the method employed could also find applications in other fields such as finance, artificial intelligence, or other physical sciences.