Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes

• URL: http://arxiv.org/abs/2309.05222v5
• Date: Sun, 2 Jun 2024 05:00:12 GMT
• Title: Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes
• Authors: Jiaxuan Zhang, Yu-Chun Wu, Guo-Ping Guo,
• Abstract summary: 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 $0.57%$ of the triangular color code. Second, our work firstly investigates the circuit-level decoding of color code lattice surgery, and gives an efficient decoding algorithm. Third, 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.
• Score: 0.6963971634605797
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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