On the computational complexity of exterior products.
Dmitri A. Ivanov · arXiv (Cornell University) · 2016
Computing the coefficients of an exterior product of two-forms of rank two is #P-hard. Specifically, a permanent of a NxN matrix may be expressed as an exterior product of N^2 two-forms of rank two in dimension 2N^2. In the context of quantum computing, such exterior products describe multi-particle scattering amplitudes of non-interacting fermions initially prepared in entangled states.