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We study locality preserving automorphisms of operator algebras on $D$-dimensional uniform lattices of prime $p$-dimensional qudits (QCA), specializing in those that are translation invariant (TI) and map every prime $p$-dimensional Pauli matrix to a tensor product of Pauli matrices (Clifford).
1902
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Kevin Walker and Zhenghan Wang, “(3+1)-TQFTs and topological insulators,” Frontiers of Physics 7
2011
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David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry (Springer, 2004)
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Michael A. Levin and Xiao-Gang Wen, “String-net condensation: a physical mechanism for topological phases,” Physical Review B 71
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B. Schumacher and R. F. Werner, “Reversible quantum cellular automata,” arXiv:quant-ph/0405174
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Jeongwan Haah, “Commuting pauli hamiltonians as maps between free modules,” Commun. Math. Phys. 324
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2014
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2017
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Kevin Walker, (2019), private communication
2019
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