A QCA for every SPT
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908587982323712 |
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| author | Fidkowski, Lukasz Haah, Jeongwan Hastings, Matthew B. |
| author_facet | Fidkowski, Lukasz Haah, Jeongwan Hastings, Matthew B. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A QCA for every SPT Fidkowski, Lukasz Haah, Jeongwan Hastings, Matthew B. Strongly Correlated Electrons Quantum Physics 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. |
| title | A QCA for every SPT |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2407.07951 |