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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.05222 |
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| _version_ | 1866916268208029696 |
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| author | Zhang, Jiaxuan Wu, Yu-Chun Guo, Guo-Ping |
| author_facet | Zhang, Jiaxuan Wu, Yu-Chun Guo, Guo-Ping |
| contents | Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical fault-tolerant quantum computing based on color codes. First, by introducing decoding graphs with error-rate-related weights, we obtained the threshold of $0.47\%$ of the 6,6,6 triangular color code under the standard circuit-level noise model, narrowing the gap to that of the surface code. Second, our work firstly investigates the circuit-level decoding of color code lattice surgery, and gives an efficient decoding algorithm, which is crucial for performing logical operations in a quantum computer with two-dimensional architectures. Lastly, a new state injection protocol of the triangular color code is proposed, reducing the output magic state error rate in one round of 15 to 1 distillation by two orders of magnitude compared to a previous rough protocol. We have also proven that our protocol offers the lowest logical error rates for state injection among all possible CSS codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05222 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes Zhang, Jiaxuan Wu, Yu-Chun Guo, Guo-Ping Quantum Physics Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical fault-tolerant quantum computing based on color codes. First, by introducing decoding graphs with error-rate-related weights, we obtained the threshold of $0.47\%$ of the 6,6,6 triangular color code under the standard circuit-level noise model, narrowing the gap to that of the surface code. Second, our work firstly investigates the circuit-level decoding of color code lattice surgery, and gives an efficient decoding algorithm, which is crucial for performing logical operations in a quantum computer with two-dimensional architectures. Lastly, a new state injection protocol of the triangular color code is proposed, reducing the output magic state error rate in one round of 15 to 1 distillation by two orders of magnitude compared to a previous rough protocol. We have also proven that our protocol offers the lowest logical error rates for state injection among all possible CSS codes. |
| title | Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.05222 |