Loop Feynman integration on a quantum computer
arxiv(2024)
摘要
This Letter 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. Oneloop 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.
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