Quantum simulation is a rapidly evolving tool with great potential for research at the frontiers of physics, and is particularly suited to be used in computationally intensive lattice simulations, such as problems with nonequilibrium. In this work, a basic scenario, namely free fermions in an expanding universe, is considered, and quantum simulations are used to perform the evolution and study the phenomena involved. Using digital quantum simulations with the Jordan-Wigner transformation and Trotter decomposition, the evolutions of fermion number density, correlation functions, polarization, and chiral condensation are analyzed. A spread out phenomenon can be observed in the simulation, which is a consequence of momentum redshift. This work also demonstrates the simplicity and convenience of using quantum simulations when studying time evolution problems.

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• Evolution of the Universe
• Quantum simulation