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.
On the singular behaviour of scattering amplitudes in quantum field theory
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abstract
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
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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.