Boundaries for the Honeycomb Code

Jeongwan Haah1 and Matthew B. Hastings1,2

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

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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.

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► References

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

[4] 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).

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

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

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

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

[9] 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).

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

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

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

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

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

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

[16] 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).

[17] 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).

[18] 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).

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

[20] 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).

[21] David Aasen, Jeongwan Haah, Zhi Li, and Roger S. K. Mong, "Measurement Quantum Cellular Automata and Anomalies in Floquet Codes", arXiv:2304.01277, (2023).

[22] 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", arXiv:2310.12981, (2023).

[23] 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).

[24] Ryohei Kobayashi and Guanyu Zhu, "Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code", arXiv:2310.06917, (2023).

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

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

[27] Brenden Roberts, Sagar Vijay, and Arpit Dua, "Geometric phases in generalized radical Floquet dynamics", arXiv:2312.04500, (2023).

[28] Moritz Lange, Pontus Havström, Basudha Srivastava, Valdemar Bergentall, Karl Hammar, Olivia Heuts, Evert van Nieuwenburg, and Mats Granath, "Data-driven decoding of quantum error correcting codes using graph neural networks", arXiv:2307.01241, (2023).

[29] David Aasen, Jeongwan Haah, Parsa Bonderson, Zhenghan Wang, and Matthew Hastings, "Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits", arXiv:2307.03715, (2023).

[30] 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 2024-06-22 09:17:27) and SAO/NASA ADS (last updated successfully 2024-06-22 09:17:28). The list may be incomplete as not all publishers provide suitable and complete citation data.