Quantum-cellular-automata pseudorandom maps

Quantum computation based on quantum-cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in which all qubits of a species evolve in parallel. We show that, in spite of its inherent constraints, a QCA system can be used to study complex quantum dynamics. To this aim, we demonstrate scalable operations on a QCA system that fulfill statistical criteria of randomness and explore which criteria of randomness can be fulfilled by operators from various QCA architectures. Other means of realizing random operators with only a few independent operators are also discussed.