Obtaining a pseudo-stochastic representation of quantum circuits with minimal negativity

In the talk the problem of finding minimal negativity for the basic elements of quantum algorithms (the initial quantum state of the register, quantum channels of elementary gates, reading measurements) for a given representation is solved by solving a linear programming problem will be considered. We also solve the problem of finding a pseudo-probabilistic representation in which total negativity of the elements of a given quantum algorithm (quantum circuit) is minimal. These problems are solved both for information-complete and overcomplete representations. The dependence of negativity on the dimension of the pseudo-stochastic representation for different types of quantum circuits is obtained.