Quantum algorithms run on current quantum computers are subjected to errors and noise caused by hardware imperfections and coupling to the environment. To know exactly how much this affects the result, a noisy circuit must be emulated on classical CPUs. This is a very tall order as in principle, a noisy quantum state must be represented with a density matrix, or by sampling over trajectories. A promising alternative is the use of tensor networks, a compressed representation of the state, to represent noisy states in an economical fashion. Positive tensor networks, also called Matrix Product Density Operators (MPDO), are promising tools to get high accuracy emulations with limited resources. They however come with their own technical constraints. The goal of this internship is to construct a complete emulation code with this type of tensor network and overcome the aforementioned difficulties, with the goal of making this simulation tool a part of Eviden’s Qaptiva, and to compare its performance with other tensor network techniques available in Qaptiva. Reference: http://arxiv.org/abs/2403.00152