Swaroop, E., Jochym-O’Connor, T., & Yoder, T. J. (2024). Universal adapters between quantum LDPC codes. arXiv preprint arXiv:2410.03628v1.
This research paper aims to address the challenge of performing joint logical measurements on quantum low-density parity-check (LDPC) codes, a crucial aspect of fault-tolerant quantum computation.
The authors propose a novel technique called "repetition code adapters," which leverages the properties of classical repetition codes and graph theory. They introduce the concept of "relative expansion" to analyze the effectiveness of their approach in maintaining code distance and ensuring the resulting deformed codes remain LDPC. The paper provides detailed algorithms and mathematical proofs to support their claims.
The proposed repetition code adapters offer a practical and efficient solution for joint logical measurements in quantum LDPC codes, simplifying the implementation of fault-tolerant quantum computation. The authors demonstrate the versatility of their approach by extending it to perform logical CNOT gates using toric code adapters.
This research significantly contributes to the field of quantum error correction by providing a universal and efficient method for logical computation in LDPC codes, paving the way for scalable and fault-tolerant quantum computers.
While the repetition code adapters offer significant advantages, the toric code adapter's O(d2) qubit overhead presents a limitation. Future research could explore alternative adapter designs for specific code families or optimize the toric code adapter for improved efficiency. Additionally, investigating the practical implementation and performance of these adapters in realistic quantum computing architectures would be valuable.
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