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arXiv · 2407.07951

A QCA for every SPT

Lukasz Fidkowski·Jeongwan Haah·Matthew B. Hastings
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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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Lukasz Fidkowski, Jeongwan Haah, Matthew B. Hastings. 2024-07-10. A QCA for every SPT. https://doi.org/10.1103/kw68-mkkd

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