General Distance Balancing for Quantum Locally Testable Codes
- URL: http://arxiv.org/abs/2305.00689v1
- Date: Mon, 1 May 2023 07:03:10 GMT
- Title: General Distance Balancing for Quantum Locally Testable Codes
- Authors: Adam Wills, Ting-Chun Lin, Min-Hsiu Hsieh
- Abstract summary: 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)
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 [
- Score: 12.547444644243544
- License: http://creativecommons.org/licenses/by/4.0/
- 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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