I am pursuing my master’s in quantum information at Sorbonne University and conducting a project on quantum causal structure and quantum cellular automata, supervised by Augustin Vanrietvelde. The objective of my project lies in proving the conjecture of causal decomposition, which stipulates an equivalence between local constraints on a quantum cellular automaton and the decomposition of a unitary channel transforming cells, particularly in an infinite-dimensional Hilbert space. This could have implications for classifying quantum circuits subjected to local constraints and our understanding of the quantum nature of spacetime carved with quantum causal structure.