How does the concept of unitarity apply to quantum cellular automata, and what challenges arise in ensuring that QCA rules preserve unitarity?

Unitarity in quantum cellular automata ensures that the evolution of the system is reversible and conserves probability, akin to the time evolution in quantum mechanics. The main challenge in ensuring unitarity is designing local update rules that are consistent with global unitarity. This often requires intricate balancing of the rules to ensure that the overall transformation of the quantum state is unitary, which can be non-trivial for complex systems with many interacting cells.