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This research establishes an algebraic framework linking invertible topological quantum field theories (TQFTs) directly to scalable quantum cellular automata, unifying disparate models under a single formalism. By demonstrating that specific dimensions yield infinite families of non-Clifford QCAs, the study provides a theoretical pathway for constructing complex high-dimensional quantum dynamics beyond current Clifford limitations.
How Invertible TQFTs Yield Scalable Quantum Cellular Automata

Constructing quantum cellular automata (QCAs) from topological quantum field theories, specifically invertible TQFTs, remains a challenge.
Meng Sun and colleagues have established an algebraic construction linking invertible topological quantum field theories (TQFTs) to quantum cellular automata (QCAs), offering a scalable method for building quantum dynamics. The work unifies previously disparate QCA…
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