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Limitations on Transversal Gates for Hypergraph Product Codes.
- Source :
- IEEE Transactions on Information Theory; Mar2022, Vol. 68 Issue 3, p1772-1781, 10p
- Publication Year :
- 2022
-
Abstract
- In a fault tolerant quantum computer, quantum codes are expected to serve the conflicting purposes of protecting quantum information while also allowing that information to be manipulated by fault-tolerant gates. We introduce a new technique for placing limitations on such gates, and apply this technique to a class of quantum codes known as hypergraph product codes contained within the vertical sector. These codes are constructed from input which is a pair of classical linear codes, and generalize the Kitaev surface code which is the hypergraph product of classical repetition codes. We provide a necessary condition on these input codes, under which the resulting hypergraph product code has transversal gates limited to the Clifford group. We conjecture that this condition is satisfied by all $[n,k,d]$ Gallagher codes with $d\ge 3$ and $k\le n/2$. This work is a generalization of an argument due to Bravyi and König, and we also conjecture this is a refinement of the recent notion of disjointness due to Jochym-O’Connor et al. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 155458615
- Full Text :
- https://doi.org/10.1109/TIT.2021.3131043