Loop Feynman integration on a quantum computer

• URL: http://arxiv.org/abs/2401.03023v1
• Date: Fri, 5 Jan 2024 19:00:04 GMT
• Title: Loop Feynman integration on a quantum computer
• Authors: Jorge J. Mart\'inez de Lejarza, Leandro Cieri, Michele Grossi, Sofia Vallecorsa, Germ\'an Rodrigo
• Abstract summary: We numerically evaluate for the first time loop Feynman integrals in a near-term quantum computer and a quantum simulator. QFIAE introduces a Quantum Neural Network (QNN) that efficiently decomposes the multidimensional integrand into its Fourier series.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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