QAIS uses a parameterized quantum circuit to allocate Monte Carlo samples along a learned non-separable density and achieves VEGAS-competitive or better accuracy on correlated integrands in simulation.
Tree-Loop Duality Relation beyond simple poles
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abstract
We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multiloop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
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Unlocking Multidimensional Integration with Quantum Adaptive Importance Sampling
QAIS uses a parameterized quantum circuit to allocate Monte Carlo samples along a learned non-separable density and achieves VEGAS-competitive or better accuracy on correlated integrands in simulation.