Ting-Chun Lin. (2024). Transversal non-Clifford gates for quantum LDPC codes on sheaves. arXiv preprint arXiv:2410.14631.
This research paper aims to address the challenge of constructing qLDPC codes that support transversal non-Clifford gates, particularly the CCZ gate, which are essential for building fault-tolerant quantum computers.
The authors utilize the concept of sheaves over cellular complexes to construct qLDPC codes. They interpret the logical operators of these codes as geometric surfaces and leverage the intersection number of these surfaces to define a trilinear map, which induces a transversal CCZ operation on the codes.
The paper presents a significant advancement in the field of quantum error correction by providing a general framework for constructing qLDPC codes with transversal CCZ gates. This approach has the potential to lead to the development of more efficient and robust fault-tolerant quantum computers.
This research contributes significantly to the field of quantum computing by providing a new avenue for constructing fault-tolerant quantum computers. The ability to implement transversal non-Clifford gates efficiently is crucial for achieving fault tolerance, and this work offers a promising approach to achieve this goal.
While the paper provides a theoretical framework, further research is needed to optimize the code parameters and develop efficient decoding algorithms for these new qLDPC codes. Additionally, exploring the practical implementation aspects of these codes and their integration into fault-tolerant quantum computing architectures will be crucial for future advancements.
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by Ting-Chun Li... alle arxiv.org 10-21-2024
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