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

C. H. Wu, C. A. Cain

Gavin K. Brennen, Jamie Williams

Rowan Brad Quni-Gudzinas

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.

Yehuda Gavriel Roth

Each neuron in the central nervous system has many dendrites, which provide input information through impulses. Assuming that a neuron's decision to continue or stop firing is made by rules applied to the dendrites' inputs, we associate neuron activity with a quantum like-cellular automaton (QLCA) concepts. Following a previous study that related the CA description with entangled states, we provide a quantum-like description of neuron activity. After reviewing and presenting the entanglement concept expressed by QLCA terminology, we propose a model that relates quantum-like measurement to consciousness. Then, we present a toy model that reviews the QLCA theory, which is adapted to our terminology. The study also focuses on implementing QLCA formalism to describe a single neuron activity.

Gerhard Grössing, Anton Zeilinger

Pablo J. Arrighi, Vincent Nesme

Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but do es it make sense as a quantum cellular automaton? That is the main question we a ddress in this paper. In every model with discrete time and space, two things ar e required in order to qualify as a cellular automaton: invariance by translatio n and locality. We prove that this locality condition is so restrictive in the q uantum case that every quantum cellular automaton constructed in this way - i. e., by linearization of a classical one - must be reversible. We also discuss some subtleties about the extent of nonlocality that can be encountered in the o ne-dimensional case; we show that, even when the quantized version is non local, still, under some conditions, we may be unable to use this nonlocality to trans mit information nonlocally.