Higher-dimensional quantum hypergraph-product codes
| Autor: | Zeng, Weilei, Pryadko, Leonid P. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Phys. Rev. Lett. 122, 230501 (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.122.230501 |
| Popis: | We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Z\'emor, and all families of toric codes on $m$-dimensional hypercubic lattices. Similar to the latter, our codes form $m$-complexes ${\cal K}_m$, with $m\ge2$. These are defined recursively, with ${\cal K}_m$ obtained as a tensor product of a complex ${\cal K}_{m-1}$ with a $1$-complex parameterized by a binary matrix. Parameters of the constructed codes are given explicitly in terms of those of binary codes associated with the matrices used in the construction. Comment: 6 pages, no figures. In version 2, a hole in the proof and several typos are corrected |
| Databáze: | arXiv |
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