A Computational Toy Model of Non-Local Information Storage in a Quantum Cellular Automaton

Can local, unitary dynamics generate the non-local information storage that holographic quantum error correction requires? This corrected version of the toy model answers with a fully reproducible exact state-vector simulation of a twelve-qubit quantum cellular automaton under the Fredkin gate. Two structural facts frame the work: standard product-state initializations are fixed points of permutation gates, and endpoint mutual information is exactly invariant under erasure of the qubits between the probes. With a documented symmetry-breaking initialization, the Fredkin dynamics generate substantial entanglement and, after erasure of up to two-thirds of the chain, retain residual segment correlations that a swap-gate control loses exactly and immediately. The simulation source ships with the paper; every reported number is reproducible. Claims are bounded by the twelve-qubit scale and by the proxy status of the diagnostics: local conditional dynamics can delocalize information across a chain in a way that pure transport cannot, measurably, before any decoder is designed.