Unlocking multidimensional integration with quantum adaptive importance sampling
Year: 2026
Type: article
Abstract: Multidimensional numerical integration is a central ingredient of theoretical predictions in high-energy physics, where multiloop Feynman diagrams and phase-space integrals are computationally demanding due to divergences and complex mathematical structures. Established Adaptive Importance Sampling methods for numerical integration, such as VEGAS, iteratively refine a grid in a separable way, dimension by dimension. This keeps the algorithm scalable but reduces performance when strong inter-variable correlations are present. In this work, we introduce a hybrid quantum-classical algorithm that performs Quantum Adaptive Importance Sampling (QAIS) for multidimensional Monte Carlo integration. Our approach uses a Parametrized Quantum Circuit to encode a non-separable Probability Density Function on a multidimensional grid and allocate samples efficiently in the integration domain. We apply the method to a sharply peaked loop Feynman integral and to multi-modal benchmark integrals. Our results show that QAIS provides an efficient route for high-precision evaluation of multidimensional integrals. Theoretical calculations in particle physics rely on multidimensional integrals that become difficult to evaluate in the presence of correlations. Here, the authors show that a hybrid quantum-classical algorithm implementing Quantum Adaptive Importance Sampling can learn correlated structures efficiently and deliver precise results for nontrivial integrals.
Source: Communications Physics
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,990
OpenAlex ID: W4414987989
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