We improve the planar honeycomb code by describing boundaries that need no additional physical connectivity, and by optimizing the shape of the qubit patch. We then benchmark the code using Monte Carlo sampling to estimate logical error rates and derive metrics including thresholds, lambdas, and teraquop qubit counts. We determine that the planar honeycomb code can create a logical qubit with one-in-a-trillion logical error rates using 7000 physical qubits at a 0.1% gate-level error rate (or 900 physical qubits given native two-qubit parity measurements). Our results cement the honeycomb code as a promising candidate for two-dimensional qubit architectures with sparse connectivity.
Estimating overheads for quantum fault-tolerance in the honeycomb code (Talk by Mike Newman)
A short history of the honeycomb code (Talk by Craig Gidney)
 Google Quantum AI. Exponential suppression of bit or phase errors with cyclic error correction. Nature, 595 (7867): 383, 2021. 10.1038/s41586-021-03588-y.
 Dave Bacon. Operator quantum error-correcting subsystems for self-correcting quantum memories. Physical Review A, 73 (1): 012340, 2006. 10.1103/PhysRevA.73.012340.
 Héctor Bombín and Miguel A Martin-Delgado. Optimal resources for topological two-dimensional stabilizer codes: Comparative study. Physical Review A, 76 (1): 012305, 2007. 10.1103/PhysRevA.76.012305.
 Christopher Chamberland, Guanyu Zhu, Theodore J Yoder, Jared B Hertzberg, and Andrew W Cross. Topological and subsystem codes on low-degree graphs with flag qubits. Physical Review X, 10 (1): 011022, 2020. 10.1103/PhysRevX.10.011022.
 Rui Chao, Michael E Beverland, Nicolas Delfosse, and Jeongwan Haah. Optimization of the surface code design for majorana-based qubits. Quantum, 4: 352, 2020. 10.22331/q-2020-10-28-352.
 Austin G Fowler. Optimal complexity correction of correlated errors in the surface code. arXiv preprint arXiv:1310.0863, 2013. 10.48550/arXiv.1310.0863.
 Craig Gidney. The stim circuit file format (.stim). https://github.com/quantumlib/Stim/blob/main/doc/file_format_stim_circuit.md, 2021b. Accessed: 2021-08-16.
 Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton. A fault-tolerant honeycomb memory. Quantum, 5: 605, 2021. 10.22331/q-2021-12-20-605.
 Yi-Chan Lee, Courtney G Brell, and Steven T Flammia. Topological quantum error correction in the kitaev honeycomb model. Journal of Statistical Mechanics: Theory and Experiment, 2017 (8): 083106, 2017. 10.1088/1742-5468/aa7ee2.
 Muyuan Li, Daniel Miller, Michael Newman, Yukai Wu, and Kenneth R. Brown. 2d compass codes. Physical Review X, 9 (2), may 2019. 10.1103/physrevx.9.021041.
 Martin Suchara, Sergey Bravyi, and Barbara Terhal. Constructions and noise threshold of topological subsystem codes. Journal of Physics A: Mathematical and Theoretical, 44 (15): 155301, 2011. 10.1088/1751-8113/44/15/155301.
 James R Wootton. Hexagonal matching codes with two-body measurements. Journal of Physics A: Mathematical and Theoretical, 55 (29): 295302, jul 2022. 10.1088/1751-8121/ac7a75.
 Craig Gidney, "A Pair Measurement Surface Code on Pentagons", arXiv:2206.12780.
 Craig Gidney, "Stability Experiments: The Overlooked Dual of Memory Experiments", arXiv:2204.13834.
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