Inplace Access to the Surface Code Y Basis

Craig Gidney

Google Quantum AI, Santa Barbara, California 93117, USA

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Abstract

In this paper, I cut the cost of Y basis measurement and initialization in the surface code by nearly an order of magnitude. Fusing twist defects diagonally across the surface code patch reaches the Y basis in $\lfloor d/2 \rfloor + 2$ rounds, without leaving the bounding box of the patch and without reducing the code distance. I use Monte Carlo sampling to benchmark the performance of the construction under circuit noise, and to analyze the distribution of logical errors. Cheap inplace Y basis measurement reduces the cost of S gates and magic state factories, and unlocks Pauli measurement tomography of surface code qubits on space-limited hardware.

The surface code is a leading contender for the quantum error correcting code to use in large scale quantum computers. Quantum error correction makes it hard to do some kinds of operations. Historically, it was easy to measure surface code qubits in the X and Z bases, but hard to reach the Y basis. This is a problem because common tasks, like computing an AND gate under superposition, involve touching the Y basis. Over time, the cost of reaching the surface code's Y basis has come down. This paper cuts the cost by nearly another factor of 10.

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Cited by

[1] Daniel Bochen Tan, Murphy Yuezhen Niu, and Craig Gidney, "A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing", arXiv:2404.18369, (2024).

[2] György P. Gehér, Ophelia Crawford, and Earl T. Campbell, "Tangling Schedules Eases Hardware Connectivity Requirements for Quantum Error Correction", PRX Quantum 5 1, 010348 (2024).

[3] Craig Gidney, Michael Newman, Peter Brooks, and Cody Jones, "Yoked surface codes", arXiv:2312.04522, (2023).

[4] Yangsen Ye, Tan He, He-Liang Huang, Zuolin Wei, Yiming Zhang, Youwei Zhao, Dachao Wu, Qingling Zhu, Huijie Guan, Sirui Cao, Fusheng Chen, Tung-Hsun Chung, Hui Deng, Daojin Fan, Ming Gong, Cheng Guo, Shaojun Guo, Lianchen Han, Na Li, Shaowei Li, Yuan Li, Futian Liang, Jin Lin, Haoran Qian, Hao Rong, Hong Su, Shiyu Wang, Yulin Wu, Yu Xu, Chong Ying, Jiale Yu, Chen Zha, Kaili Zhang, Yong-Heng Huo, Chao-Yang Lu, Cheng-Zhi Peng, Xiaobo Zhu, and Jian-Wei Pan, "Logical Magic State Preparation with Fidelity beyond the Distillation Threshold on a Superconducting Quantum Processor", Physical Review Letters 131 21, 210603 (2023).

[5] Jiaxuan Zhang, Yu-Chun Wu, and Guo-Ping Guo, "Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes", arXiv:2309.05222, (2023).

[6] Craig Gidney, "Cleaner magic states with hook injection", arXiv:2302.12292, (2023).

[7] Michael E. Beverland, Shilin Huang, and Vadym Kliuchnikov, "Fault tolerance of stabilizer channels", arXiv:2401.12017, (2024).

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[9] György P. Gehér, Campbell McLauchlan, Earl T. Campbell, Alexandra E. Moylett, and Ophelia Crawford, "Error-corrected Hadamard gate simulated at the circuit level", arXiv:2312.11605, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2024-05-26 15:47:09). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2024-05-26 15:47:08).