A QCA for every SPT
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.07951
- arXiv:
- arXiv:2407.07951
- Bibcode:
- 2024arXiv240707951F
- Keywords:
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- Condensed Matter - Strongly Correlated Electrons;
- Quantum Physics