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arXiv · 2305.00689

General Distance Balancing for Quantum Locally Testable Codes

Adam Wills·Ting-Chun Lin·Min-Hsiu Hsieh
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Abstract

In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new soundness of the quantum code is at least the old soundness divided by the classical code length (up to a constant factor). This allows us to use any classical code with independent checks when distance balancing, where previously only the repetition code had been considered for qLTCs. By using a good classical LDPC code, we are able to grow the dimension of the hypersphere product codes arXiv:1608.05089 [quant-ph] and the hemicubic codes arXiv:1911.03069 [quant-ph] while maintaining their distance and locality, but at the expense of soundness. From this, and also by distance balancing a chain complex of Cross et al. arXiv:2209.11405 [cs.IT], we obtain quantum locally testable codes of new parameters.

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Adam Wills, Ting-Chun Lin, Min-Hsiu Hsieh. 2023-05-01. General Distance Balancing for Quantum Locally Testable Codes. https://arxiv.org/abs/2305.00689

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