Benchmarking the Planar Honeycomb Code

Craig Gidney1, Michael Newman1, and Matt McEwen1,2

1Google Quantum AI, Santa Barbara, California 93117, USA
2University of California, Santa Barbara, 93106, USA

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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)

In this paper, we benchmarked a new version of the honeycomb code. The old version of the honeycomb code couldn't fit on a flat surface. It had to be wrapped around a donut. That was a problem because many quantum computer architectures place qubits on a flat surface, not on donuts. Although the donut problem was fixed, the fix required changes that we were worried might seriously hurt the performance of the honeycomb code. However, the result of this paper is that the new honeycomb code still performs very well. This shows the honeycomb code is a viable error correcting code candidate for large scale quantum computer architectures, even ones that place qubits on a flat surface.

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► References

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[1] Suhas Vittal, Poulami Das, and Moinuddin Qureshi, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.

[2] Younghun Kim, Jeongsoo Kang, and Younghun Kwon, "Design of quantum error correcting code for biased error on heavy-hexagon structure", Quantum Information Processing 22 6, 230 (2023).

[3] 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).

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

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

[6] 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).

[7] Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J. Williamson, "Pauli topological subsystem codes from Abelian anyon theories", arXiv:2211.03798, (2022).

[8] Craig Gidney, "A Pair Measurement Surface Code on Pentagons", arXiv:2206.12780, (2022).

[9] Stefano Paesani and Benjamin J. Brown, "High-Threshold Quantum Computing by Fusing One-Dimensional Cluster States", Physical Review Letters 131 12, 120603 (2023).

[10] Craig Gidney and Dave Bacon, "Less Bacon More Threshold", arXiv:2305.12046, (2023).

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

[12] 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).

The above citations are from Crossref's cited-by service (last updated successfully 2023-10-01 02:50:28) and SAO/NASA ADS (last updated successfully 2023-10-01 02:50:28). The list may be incomplete as not all publishers provide suitable and complete citation data.