A Fault-Tolerant Honeycomb Memory

Craig Gidney; Michael Newman; Austin Fowler; Michael Broughton

doi:10.22331/q-2021-12-20-605

A Fault-Tolerant Honeycomb Memory

Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton

Google Quantum AI, Santa Barbara, California 93117, USA

Published:	2021-12-20, volume 5, page 605
Eprint:	arXiv:2108.10457v2
Doi:	https://doi.org/10.22331/q-2021-12-20-605
Citation:	Quantum 5, 605 (2021).

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Abstract

Recently, Hastings & Haah introduced a quantum memory defined on the honeycomb lattice. Remarkably, this honeycomb code assembles weight-six parity checks using only two-local measurements. The sparse connectivity and two-local measurements are desirable features for certain hardware, while the weight-six parity checks enable robust performance in the circuit model.
In this work, we quantify the robustness of logical qubits preserved by the honeycomb code using a correlated minimum-weight perfect-matching decoder. Using Monte Carlo sampling, we estimate the honeycomb code's threshold in different error models, and project how efficiently it can reach the "teraquop regime" where trillions of quantum logical operations can be executed reliably. We perform the same estimates for the rotated surface code, and find a threshold of $0.2\%-0.3\%$ for the honeycomb code compared to a threshold of $0.5\%-0.7\%$ for the surface code in a controlled-not circuit model. In a circuit model with native two-body measurements, the honeycomb code achieves a threshold of $1.5\% \lt p \lt 2.0\%$, where $p$ is the collective error rate of the two-body measurement gate - including both measurement and correlated data depolarization error processes. With such gates at a physical error rate of $10^{−3}$, we project that the honeycomb code can reach the teraquop regime with only $600$ physical qubits.

Featured image: Key elements of the honeycomb code.

Popular summary

We checked how well a new quantum error correcting code works. The new code is called the honeycomb code and was found by researchers at Microsoft. We did simulations to estimate the quality and quantity of noisy qubits needed to reach error rates as low as 1 in a trillion. We compared the honeycomb code to the surface code (the current state of the art).

We used new open source tools: Stim and PyMatching. These tools allowed us to get prototype results in weeks, instead of months, even though the honeycomb code is a very recent and unusual quantum code.

We found that the honeycomb code is slightly worse than the surface code. However, the honeycomb code works on hardware with fewer connections between qubits than the surface code. Also, its performance is very good when the hardware can directly measure two-qubit parities – better than previous codes built entirely out of two-qubit parity measurements. This makes the honeycomb code interesting for quantum computer architectures with low connectivity or native parity measurements.

► BibTeX data

@article{Gidney2021faulttolerant,
  doi = {10.22331/q-2021-12-20-605},
  url = {https://doi.org/10.22331/q-2021-12-20-605},
  title = {A {F}ault-{T}olerant {H}oneycomb {M}emory},
  author = {Gidney, Craig and Newman, Michael and Fowler, Austin and Broughton, Michael},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {605},
  month = dec,
  year = {2021}
}

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Cited by

[1] 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).

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

[3] Oscar Higgott, "PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[4] James R Wootton, "Hexagonal matching codes with two-body measurements", Journal of Physics A: Mathematical and Theoretical 55 29, 295302 (2022).

[5] 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).

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

[8] Edward H. Chen, Theodore J. Yoder, Youngseok Kim, Neereja Sundaresan, Srikanth Srinivasan, Muyuan Li, Antonio D. Córcoles, Andrew W. Cross, and Maika Takita, "Calibrated Decoders for Experimental Quantum Error Correction", Physical Review Letters 128 11, 110504 (2022).

[9] Jeongwan Haah and Matthew B. Hastings, "Boundaries for the Honeycomb Code", Quantum 6, 693 (2022).

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

[11] Benjamin A. Cordier, Nicolas P. D. Sawaya, Gian Giacomo Guerreschi, and Shannon K. McWeeney, "Biology and medicine in the landscape of quantum advantages", Journal of The Royal Society Interface 19 196, 20220541 (2022).

[12] Julia Wildeboer, Thomas Iadecola, and Dominic J. Williamson, "Symmetry-Protected Infinite-Temperature Quantum Memory from Subsystem Codes", PRX Quantum 3 2, 020330 (2022).

[13] Oscar Higgott, Thomas C. Bohdanowicz, Aleksander Kubica, Steven T. Flammia, and Earl T. Campbell, "Fragile boundaries of tailored surface codes and improved decoding of circuit-level noise", arXiv:2203.04948, (2022).

[14] Benjamin A. Cordier, Nicolas P. D. Sawaya, Gian G. Guerreschi, and Shannon K. McWeeney, "Biology and medicine in the landscape of quantum advantages", arXiv:2112.00760, (2021).

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

[16] Jason Bennett, "Fractons: gauging spin models and tensor gauge theory", arXiv:2206.14028, (2022).

[17] Andrew J. Landahl and Benjamin C. A. Morrison, "Logical Majorana fermions for fault-tolerant quantum simulation", arXiv:2110.10280, (2021).

[18] Oscar Higgott and Craig Gidney, "Sparse Blossom: correcting a million errors per core second with minimum-weight matching", arXiv:2303.15933, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-09 09:02:01) and SAO/NASA ADS (last updated successfully 2023-06-09 09:02:02). The list may be incomplete as not all publishers provide suitable and complete citation data.

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