A Pair Measurement Surface Code on Pentagons

Craig Gidney

Google Quantum AI, Santa Barbara, California 93117, USA

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In this paper, I present a way to compile the surface code into two-body parity measurements ("pair measurements"), where the pair measurements run along the edges of a Cairo pentagonal tiling. The resulting circuit improves on prior work by Chao et al. by using fewer pair measurements per four-body stabilizer measurement (5 instead of 6) and fewer time steps per round of stabilizer measurement (6 instead of 10). Using Monte Carlo sampling, I show that these improvements increase the threshold of the surface code when compiling into pair measurements from $\approx 0.2\%$ to $\approx 0.4\%$, and also that they improve the teraquop footprint at a $0.1\%$ physical gate error rate from $\approx6000$ qubits to $\approx3000$ qubits. However, I also show that the teraquop footprint of Chao et al's construction improves more quickly than mine as physical error rate decreases, and is likely better below a physical gate error rate of $\approx 0.03\%$ (due to bidirectional hook errors in my construction). I also compare to the planar honeycomb code, showing that although this work does noticeably reduce the gap between the surface code and the honeycomb code (when compiling into pair measurements), the honeycomb code is still more efficient (threshold $\approx 0.8\%$, teraquop footprint at $0.1\%$ of $\approx 1000$).

Surface codes are an important type of quantum error correcting code. Usually surface codes are implemented using reversible interactions, like controlled-not gates. But some hardware architectures could be based around interactions that are irreversible, like two qubit parity measurements. This paper describes a better way to build a surface code for those architectures. The pairs of qubits interacted by the construction form the edges of a Cairo pentagonal tiling.

► BibTeX data

► References

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

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

[3] 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).

[4] Oscar Higgott and Nikolas P. Breuckmann, "Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes", arXiv:2308.03750, (2023).

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

[6] Hector Bombin, Chris Dawson, Terry Farrelly, Yehua Liu, Naomi Nickerson, Mihir Pant, Fernando Pastawski, and Sam Roberts, "Fault-tolerant complexes", arXiv:2308.07844, (2023).

[7] Nicolas Delfosse, Andres Paz, Alexander Vaschillo, and Krysta M. Svore, "How to choose a decoder for a fault-tolerant quantum computer? The speed vs accuracy trade-off", arXiv:2310.15313, (2023).

[8] Alex Townsend-Teague, Julio Magdalena de la Fuente, and Markus Kesselring, "Floquetifying the Colour Code", arXiv:2307.11136, (2023).

[9] Hector Bombin, Daniel Litinski, Naomi Nickerson, Fernando Pastawski, and Sam Roberts, "Unifying flavors of fault tolerance with the ZX calculus", arXiv:2303.08829, (2023).

[10] Nicolas Delfosse and Adam Paetznick, "Spacetime codes of Clifford circuits", arXiv:2304.05943, (2023).

[11] Matthew J. Reagor, Thomas C. Bohdanowicz, David Rodriguez Perez, Eyob A. Sete, and William J. Zeng, "Hardware optimized parity check gates for superconducting surface codes", arXiv:2211.06382, (2022).

[12] Jiaxin Huang, Sarah Meng Li, Lia Yeh, Aleks Kissinger, Michele Mosca, and Michael Vasmer, "Graphical CSS Code Transformation Using ZX Calculus", arXiv:2307.02437, (2023).

[13] Craig Gidney and Cody Jones, "New circuits and an open source decoder for the color code", arXiv:2312.08813, (2023).

[14] Tuomas Laakkonen, Konstantinos Meichanetzidis, and John van de Wetering, "Picturing Counting Reductions with the ZH-Calculus", arXiv:2304.02524, (2023).

[15] Nicolas Delfosse and Adam Paetznick, "Simulation of noisy Clifford circuits without fault propagation", arXiv:2309.15345, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-21 08:36:03) and SAO/NASA ADS (last updated successfully 2024-05-21 08:36:04). The list may be incomplete as not all publishers provide suitable and complete citation data.