Monte Carlo integration is a fundamental method underpinning Monte Carlo simulations in high-energy physics (HEP). In this talk, I will present universal "building blocks" for quantum-enhanced integration of generic cross sections in HEP, based on Fourier Quantum Monte Carlo Integration. Leveraging Quantinuum’s Quantum Monte Carlo Integration engine, this approach enables the efficient generation of quantum circuits for these calculations, achieving a quadratic speed-up in root mean-squared error convergence compared to classical methods. To illustrate its impact, I will walk through a concrete example of a 1→3 decay process, demonstrating how quantum algorithms can enhance integral estimation in HEP and potentially reshape computational strategies in the future.