Boundaries for the Honeycomb Code

Jeongwan Haah; Matthew B. Hastings

doi:10.22331/q-2022-04-21-693

Boundaries for the Honeycomb Code

Jeongwan Haah¹ and Matthew B. Hastings^1,2

¹Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA
²Station Q, Microsoft Quantum, Santa Barbara, CA 93106-6105, USA

Published:	2022-04-21, volume 6, page 693
Eprint:	arXiv:2110.09545v2
Doi:	https://doi.org/10.22331/q-2022-04-21-693
Citation:	Quantum 6, 693 (2022).

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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

@article{Haah2022boundarieshoneycomb,
  doi = {10.22331/q-2022-04-21-693},
  url = {https://doi.org/10.22331/q-2022-04-21-693},
  title = {Boundaries for the {H}oneycomb {C}ode},
  author = {Haah, Jeongwan and Hastings, Matthew B.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {693},
  month = apr,
  year = {2022}
}

► 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] Ammar Jahin, Andy C. Y. Li, Thomas Iadecola, Peter P. Orth, Gabriel N. Perdue, Alexandru Macridin, M. Sohaib Alam, and Norm M. Tubman, "Fermionic approach to variational quantum simulation of Kitaev spin models", Physical Review A 106 2, 022434 (2022).

[2] Basudha Srivastava, Anton Frisk Kockum, and Mats Granath, "The XYZ2 hexagonal stabilizer code", Quantum 6, 698 (2022).

[3] Craig Gidney, Michael Newman, and Matt McEwen, "Benchmarking the Planar Honeycomb Code", Quantum 6, 813 (2022).

[4] David Aasen, Zhenghan Wang, and Matthew B. Hastings, "Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes", Physical Review B 106 8, 085122 (2022).

[5] Craig Gidney, "Stability Experiments: The Overlooked Dual of Memory Experiments", Quantum 6, 786 (2022).

[6] Andreas Bartschi and Stephan Eidenbenz, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 87 (2022) ISBN:978-1-6654-9113-6.

[7] Matt McEwen, Dave Bacon, and Craig Gidney, "Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics", arXiv:2302.02192, (2023).

[8] 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", PRX Quantum 4 1, 010310 (2023).

[9] Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton, "A Fault-Tolerant Honeycomb Memory", Quantum 5, 605 (2021).

[10] Christophe Vuillot, "Planar Floquet Codes", arXiv:2110.05348, (2021).

[11] Andreas Bärtschi and Stephan Eidenbenz, "Short-Depth Circuits for Dicke State Preparation", arXiv:2207.09998, (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-05 12:02:00) and SAO/NASA ADS (last updated successfully 2023-06-05 12:02:01). The list may be incomplete as not all publishers provide suitable and complete citation data.

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