We establish a link between stabilizer states, rank, and higher-order Fourier analysis -- still-developing area of mathematics that grew out Gowers's celebrated Fourier-analytic proof Szemer\'edi's theorem \cite{gowers1998new}. observe $n$-qudit states are so-called nonclassical quadratic phase functions (defined on affine subspaces $\mathbb{F}_p^n$ where $p$ is the dimension qudit) which funda...

The steady trend of complication mining and geological factors in underground coal at the same time processes intensification cause growth dynamic manifestations natural mining, such as sudden gas outbursts, rock bursts, collapses, leading to dust explosions fires. This requires developing models different phenomena manifestation risks, which enable improving process safety a enterprise. In thi...