Quantum integration of decay rates at second order in perturbation theory

We present the first quantum computation of a total decay rate in high-energy physics at second order in perturbative quantum field theory. This work underscores the confluence of two recent cutting-edge advances. On the one hand, the quantum integration algorithm Quantum Fourier Iterative Amplitude Estimation (QFIAE), which efficiently decomposes the target function into its Fourier series through a quantum neural network before quantumly integrating the corresponding Fourier components. On the other hand, causal unitary in the loop-tree duality (LTD), which exploits the causal properties of vacuum amplitudes in LTD to coherently generate all contributions with different numbers of final-state particles to a scattering or decay process, leading to singularity-free integrands that are well suited for Fourier decomposition. We test the performance of the quantum algorithm with benchmark decay rates in a quantum simulator and in quantum hardware, and find accurate theoretical predictions in both settings.