Ide, B., Gowda, M. G., Nadkarni, P. J., & Dauphinais, G. (2024, October 3). Fault-tolerant logical measurements via homological measurement. arXiv.org. https://arxiv.org/abs/2410.02753v1
This paper aims to develop a resource-efficient and fault-tolerant method for measuring logical Pauli operators in CSS stabilizer codes, particularly focusing on quantum LDPC codes, which are promising candidates for fault-tolerant quantum computation.
The authors introduce a mathematical framework called "homological measurement" based on the algebraic description of CSS codes as chain complexes. They utilize concepts from homological algebra, such as mapping cones and long exact sequences, to analyze the properties of cone codes and design a specific protocol called "edge expanded homological measurement." This protocol leverages graph theory principles, including the Cheeger constant and cellulation, to optimize the measurement process and minimize resource requirements.
The homological measurement framework provides a powerful tool for understanding and designing fault-tolerant measurement protocols for CSS stabilizer codes. The edge expanded homological measurement protocol offers a resource-efficient solution for measuring logical Pauli operators in quantum LDPC codes, paving the way for practical implementations of fault-tolerant quantum computation.
This research significantly contributes to the field of quantum error correction by introducing a novel framework and a practical protocol for fault-tolerant logical measurements in quantum LDPC codes. The reduced resource overhead achieved by the proposed method addresses a critical challenge in realizing scalable fault-tolerant quantum computers.
The paper primarily focuses on measuring individual logical operators. Further research could explore extending the homological measurement framework to efficiently perform joint measurements on multiple logical operators simultaneously. Additionally, investigating the application of this framework to other types of quantum codes beyond CSS codes could lead to further advancements in fault-tolerant quantum computation.
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