1Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA
2Station Q, Microsoft Quantum, Santa Barbara, CA 93106-6105, USA
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We introduce a simple construction of boundary conditions for the honeycomb code [1] that uses only pairwise checks and allows parallelogram geometries at the cost of modifying the bulk measurement sequence. We discuss small instances of the code.
► BibTeX data
► References
[1] M. B. Hastings and J. Haah, “Dynamically generated logical qubits,” arXiv preprint (2021), 2107.02194.
https://doi.org/10.22331/q-2021-10-19-564
arXiv:2107.02194
[2] A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals of Physics 321, 2–111 (2006), cond-mat/0506438.
https://doi.org/10.1016/j.aop.2005.10.005
arXiv:cond-mat/0506438
[3] J. R. Wootton, “A family of stabilizer codes for $D({mathbb Z}_2)$ anyons and Majorana modes,” J. Phys. A: Math. Theor. 48, 215302 (2015), arXiv:1501.07779.
https://doi.org/10.1088/1751-8113/48/21/215302
arXiv:1501.07779
[4] R. Chao, M. E. Beverland, N. Delfosse, and J. Haah, “Optimization of the surface code design for majorana-based qubits,” Quantum 4, 352 (2020), 2007.00307.
https://doi.org/10.22331/q-2020-10-28-352
arXiv:2007.00307
[5] C. Gidney, M. Newman, A. Fowler, and M. Broughton, “A fault-tolerant honeycomb memory,” arXiv:2108.10457.
https://doi.org/10.22331/q-2021-12-20-605
arXiv:2108.10457
[6] S. B. Bravyi and A. Y. Kitaev, “Quantum codes on a lattice with boundary,” quant-ph/9811052.
arXiv:quant-ph/9811052
[7] M. H. Freedman and D. A. Meyer, “Projective plane and planar quantum codes,” quant-ph/9810055.
arXiv:quant-ph/9810055
[8] E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory,” J. Math. Phys. 43, 4452–4505 (2002), quant-ph/0110143.
https://doi.org/10.1063/1.1499754
arXiv:quant-ph/0110143
[9] A. Paetznick et. al., in preparation.
[10] C. Vuillot, “Planar floquet codes,” arXiv:2110.05348.
arXiv:2110.05348
[11] D. Gottesman, “Fault-tolerant quantum computation with higher-dimensional systems,” Chaos Solitons Fractals 10, 1749–1758 (1999), arXiv:quant-ph/9802007.
https://doi.org/10.1016/S0960-0779(98)00218-5
arXiv:quant-ph/9802007
[12] Y. Li, “A magic state’s fidelity can be superior to the operations that created it,” New J. Phys. 17, 023037 (2015), 1410.7808.
https://doi.org/10.1088/1367-2630/17/2/023037
arXiv:1410.7808
[13] H. Bombin and M. A. Martin-Delgado, “Topological quantum distillation,” Physical review letters 97, 180501 (2006), quant-ph/0605138.
https://doi.org/10.1103/PhysRevLett.97.180501
arXiv:quant-ph/0605138
[14] H. Bombín and M. A. Martin-Delgado, “Optimal resources for topological two-dimensional stabilizer codes: Comparative study,” Physical Review A 76, 012305 (2007), arXiv:quant-ph/0703272.
https://doi.org/10.1103/PhysRevA.76.012305
arXiv:quant-ph/0703272
Cited by
[1] Basudha Srivastava, Anton Frisk Kockum, and Mats Granath, “The XYZ2 hexagonal stabilizer code”, arXiv:2112.06036, Quantum 6, 698 (2022).
[2] Christophe Vuillot, “Planar Floquet Codes”, arXiv:2110.05348.
[3] Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton, “A Fault-Tolerant Honeycomb Memory”, arXiv:2108.10457.
[4] Adam Paetznick, Christina Knapp, Nicolas Delfosse, Bela Bauer, Jeongwan Haah, Matthew B. Hastings, and Marcus P. da Silva, “Performance of planar Floquet codes with Majorana-based qubits”, arXiv:2202.11829.
[5] Craig Gidney, Michael Newman, and Matt McEwen, “Benchmarking the Planar Honeycomb Code”, arXiv:2202.11845.
[6] Craig Gidney, “Stability Experiments: The Overlooked Dual of Memory Experiments”, arXiv:2204.13834.
The above citations are from Crossref’s cited-by service (last updated successfully 2022-05-14 10:01:19) and SAO/NASA ADS (last updated successfully 2022-05-14 10:01:20). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.