43rd International Conference on High Energy Physics

Multi-Dimensional Integration with Quantum Adaptive Importance Sampling

30 Jul 2026, 14:30

15m

Room #9 (Praiamar Natal Hotel & Convention)

Talk Artificial Intelligence, Machine Learning and Quantum Computing in HEP Artificial Intelligence, Machine Learning and Quantum Computing in HEP

Speaker

Konstantinos Pyretzidis (IFIC ( UV-CSIC ))

Description

Perturbative Quantum Field Theory is central for performing precise predictions of observables at high-energy colliders. Fundamental concepts in this framework, such as Loop Feynman diagrams and the phase-space, require evaluating multidimensional integrals. The standard approach relies on adaptive importance sampling, notably the VEGAS algorithm, which updates a multidimensional grid. Because the cost of handling each grid cell grows exponentially with the integral's dimensions, the Probability Density Function (PDF) model is simplified to a separable product of PDFs, factorized along each integration variable's axis.

We present a hybrid quantum-classical algorithm that performs Quantum Adaptive Importance Sampling (QAIS). By using the exponentially sized Hilbert space of a Parameterized Quantum Circuit (PQC), we manipulate the PDF over the grid in its entirety. With adequate expressivity and entanglement, we capture correlations among integrand variables, bypassing the separable PDF assumption. By optimizing the PQC, we adapt and load a PDF that approximates the integrand's behavior. Direct sampling allocates samples into important regions, enabling accurate integral estimation. We test QAIS on benchmark integrals and Loop Feynman integrals, comparing against VEGAS's proposal PDF at fixed sample sizes.

References

K. Pyretzidis, J.J. Martínez de Lejarza, G. Rodrigo, Unlocking Multi-Dimensional Integration with Quantum Adaptive Importance Sampling, e-Print: 2506.19965 [quant-ph]