Quantum cellular automata for word statistics facilitated by quantum correlations

We propose an iterative algorithm to investigate the cooperative evolution dominated by information encoded within state spaces in a random quantum cellular automaton. Inspired by the 2-gram model in statistical linguistics, the updates of quantum states are determined by a given corpus, which serves as the interactions to induce quantum correlations. These local cooperative interactions lead to block-diagonal evolution quantified by the entanglement asymmetry. We evaluate the influence of two-site gates on the iteration process and reveal the associated search speedup. Crucially, we demonstrate the information scrambling dependent of gate sampling, uncovering an intriguing bond percolation. Our results provide an adaptive paradigm for quantum search algorithms and random many-body dynamics.