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}
}

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[1] Julio C. Magdalena de la Fuente, Josias Old, Alex Townsend-Teague, Manuel Rispler, Jens Eisert, and Markus Müller, "XYZ Ruby Code: Making a Case for a Three-Colored Graphical Calculus for Quantum Error Correction in Spacetime", PRX Quantum 6 1, 010360 (2025).

[2] Adithya Sriram, Tibor Rakovszky, Vedika Khemani, and Matteo Ippoliti, "Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model", Physical Review B 108 9, 094304 (2023).

[3] Zhehao Zhang, David Aasen, and Sagar Vijay, "X -cube Floquet code: A dynamical quantum error correcting code with a subextensive number of logical qubits", Physical Review B 108 20, 205116 (2023).

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

[5] Margarita Davydova, Nathanan Tantivasadakarn, and Shankar Balasubramanian, "Floquet Codes without Parent Subsystem Codes", PRX Quantum 4 2, 020341 (2023).

[6] 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).

[7] Shouzhen Gu, Alex Retzker, and Aleksander Kubica, "Fault-tolerant quantum architectures based on erasure qubits", Physical Review Research 7 1, 013249 (2025).

[8] Oscar Higgott and Nikolas P. Breuckmann, "Constructions and Performance of Hyperbolic and Semi-Hyperbolic Floquet Codes", PRX Quantum 5 4, 040327 (2024).

[9] Matt McEwen, Dave Bacon, and Craig Gidney, "Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics", Quantum 7, 1172 (2023).

[10] Joseph Sullivan, Rui Wen, and Andrew C. Potter, "Floquet codes and phases in twist-defect networks", Physical Review B 108 19, 195134 (2023).

[11] César Benito, Esperanza López, Borja Peropadre, and Alejandro Bermudez, "Comparative study of quantum error correction strategies for the heavy-hexagonal lattice", Quantum 9, 1623 (2025).

[12] Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J. Williamson, "Pauli topological subsystem codes from Abelian anyon theories", Quantum 7, 1137 (2023).

[13] 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).

[14] Grace M. Sommers, David A. Huse, and Michael J. Gullans, "Crystalline Quantum Circuits", PRX Quantum 4 3, 030313 (2023).

[15] Ali Lavasani, Zhu-Xi Luo, and Sagar Vijay, "Monitored quantum dynamics and the Kitaev spin liquid", Physical Review B 108 11, 115135 (2023).

[16] Linnea Grans-Samuelsson, Ryan V. Mishmash, David Aasen, Christina Knapp, Bela Bauer, Brad Lackey, Marcus P. da Silva, and Parsa Bonderson, "Improved Pairwise Measurement-Based Surface Code", Quantum 8, 1429 (2024).

[17] Andreas Bauer, "Topological error correcting processes from fixed-point path integrals", Quantum 8, 1288 (2024).

[18] Asmae Benhemou, Kaavya Sahay, Lingling Lao, and Benjamin J. Brown, "Minimising surface-code failures using a color-code decoder", Quantum 9, 1632 (2025).

[19] Bence Hetényi and James R. Wootton, "Tailoring quantum error correction to spin qubits", Physical Review A 109 3, 032433 (2024).

[20] Hector Bombin, Daniel Litinski, Naomi Nickerson, Fernando Pastawski, and Sam Roberts, "Unifying flavors of fault tolerance with the ZX calculus", Quantum 8, 1379 (2024).

[21] Andreas Bauer, "x+y Floquet code: A simple example for topological quantum computation in the path-integral approach", Physical Review A 111 3, 032413 (2025).

[22] Campbell McLauchlan, György P. Gehér, and Alexandra E. Moylett, "Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements", Quantum 8, 1562 (2024).

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

[24] Arpit Dua, Nathanan Tantivasadakarn, Joseph Sullivan, and Tyler D. Ellison, "Engineering 3D Floquet Codes by Rewinding", PRX Quantum 5 2, 020305 (2024).

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

[26] Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, and Benjamin J. Brown, "Anyon Condensation and the Color Code", PRX Quantum 5 1, 010342 (2024).

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

[28] Ryohei Kobayashi and Guanyu Zhu, "Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code", PRX Quantum 5 2, 020360 (2024).

[29] Margarita Davydova, Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen, "Quantum computation from dynamic automorphism codes", Quantum 8, 1448 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2025-05-12 11:58:34). The list may be incomplete as not all publishers provide suitable and complete citation data.

On SAO/NASA ADS no data on citing works was found (last attempt 2025-05-12 11:58:34).

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