A QCA for every SPT

• URL: http://arxiv.org/abs/2407.07951v2
• Date: Fri, 22 Nov 2024 01:22:28 GMT
• Title: A QCA for every SPT
• Authors: Lukasz Fidkowski, Jeongwan Haah, Matthew B. Hastings,
• Abstract summary: In three dimensions, there is a nontrivial quantum cellular automaton (QCA) which disentangles the three-fermion Walker--Wang model. Some of our QCA are Clifford, and we relate these to a classification theorem of Clifford QCA. We identify Clifford QCA in $4m+1$ dimensions, for which we find a low-depth circuit description using non-Clifford gates but not with Clifford gates.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In three dimensions, there is a nontrivial quantum cellular automaton (QCA) which disentangles the three-fermion Walker--Wang model, a model whose action depends on Stiefel--Whitney classes of the spacetime manifold. Here we present a conjectured generalization to higher dimensions. For an arbitrary symmetry protected topological phase of time reversal whose action depends on Stiefel--Whitney classes, we construct a corresponding QCA that we conjecture disentangles that phase. Some of our QCA are Clifford, and we relate these to a classification theorem of Clifford QCA. We identify Clifford QCA in $4m+1$ dimensions, for which we find a low-depth circuit description using non-Clifford gates but not with Clifford gates.

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