9 C
New York

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

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


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)

[embedded content]

A short history of the honeycomb code (Talk by Craig Gidney)

[embedded content]

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.

► BibTeX data

► References

[1] 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.

[2] Dave Bacon. Operator quantum error-correcting subsystems for self-correcting quantum memories. Physical Review A, 73 (1): 012340, 2006. 10.1103/​PhysRevA.73.012340.

[3] 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.

[4] 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.

[5] 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.

[6] Austin G Fowler. Optimal complexity correction of correlated errors in the surface code. arXiv preprint arXiv:1310.0863, 2013. 10.48550/​arXiv.1310.0863.

[7] Craig Gidney. Stim: a fast stabilizer circuit simulator. Quantum, 5: 497, July 2021a. ISSN 2521-327X. 10.22331/​q-2021-07-06-497.

[8] 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.

[9] 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.

[10] Craig Gidney, Michael Newman, and Matt Mcewen. Data for “Benchmarking the Planar Honeycomb Code”. Zenodo, September 2022. 10.5281/​zenodo.7072889.

[11] Jeongwan Haah and Matthew B Hastings. Boundaries for the honeycomb code. Quantum, 6: 693, 2022. 10.22331/​q-2022-04-21-693.

[12] Matthew B Hastings and Jeongwan Haah. Dynamically generated logical qubits. Quantum, 5: 564, 2021. 10.22331/​q-2021-10-19-564.

[13] Alexei Kitaev. Anyons in an exactly solved model and beyond. Annals of Physics, 321 (1): 2–111, 2006. 10.1016/​j.aop.2005.10.005.

[14] 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.

[15] 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.

[16] 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.

[17] 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.

Cited by

[1] Craig Gidney, “A Pair Measurement Surface Code on Pentagons”, arXiv:2206.12780.

[2] Craig Gidney, “Stability Experiments: The Overlooked Dual of Memory Experiments”, arXiv:2204.13834.

The above citations are from SAO/NASA ADS (last updated successfully 2022-09-21 12:03:37). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2022-09-21 12:03:34: Could not fetch cited-by data for 10.22331/q-2022-09-21-813 from Crossref. This is normal if the DOI was registered recently.

  • Coinsmart. Europe’s Best Bitcoin and Crypto Exchange.Click Here
  • Platoblockchain. Web3 Metaverse Intelligence. Knowledge Amplified. Access Here.
  • Source: https://quantum-journal.org/papers/q-2022-09-21-813/

Latest Intelligence


Latest Intelligence