Quantum Cellular Automata (QCA) are lattices with a quantum system at each site that have discrete time evolution with finite information propagation speed. They have been showed very promising, for instance, as a model for lattices evolving via time-dependent Hamiltonians. In this work we will explain that 1D QCA are equivalent to Matrix Product Unitaries and classify them according to their information flow. This allows to realize that all 1D QCA are compositions of finite depth quantum circuits and shift operations

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutors: Sofyan Iblisdir, Alberto Ruiz de Alarcón