Tradeoff Constructions for Quantum Locally Testable Codes

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In this work, we continue the search for quantum locally testable codes (qLTCs) of new parameters by presenting three constructions that can make new qLTCs from old.

• The first analyses the soundness of a quantum code under Hastings' weight reduction construction for qLDPC codes arXiv:2102.10030 to give a weight reduction procedure for qLTCs.
• Secondly, we describe a novel `soundness amplification' procedure for qLTCs which can increase the soundness of any qLTC to a constant while preserving its distance and dimension, with an impact only felt on its locality.
• Finally, we apply the AEL distance amplification construction to the case of qLTCs for the first time which can turn a high-distance qLTC into one with linear distance, at the expense of other parameters.