Quantum computing applications in cosmology

Quantum computing has become increasingly popular in recent years, since it has the potential to outperform classical computation, at least in specific tasks. In principle, this advantage could help many fields of physics research, such as cosmology. Numerical simulations of cosmological observables have become more and more complex and demanding in terms of resources. Quantum computers might help and this thesis is devoted to develop this idea within the NISQ era and its limitations. The work focuses both on introducing quantum algorithms in existing classical codes and on developing a hybrid code to simulate the evolution of DM. The first analysis substitutes the Fast Fourier Transform with the Quantum Fourier Transform to compute the matter power spectrum and shows that the current generation of quantum computers is not enough to produce physically relevant results. The second analysis considers the development of a hybrid classical-quantum code to solve Schr\"{o}dinger-Poisson equations in one dimension. Results in ideal simulators prove that the code can be used to find the correct solution, while real quantum computers allow recovering part of the expected signal only at the price of introducing approximations.