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Quantum Locally Testable Code with Constant Soundness
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DOI：10.22331/q-2024-10-18-1501.png)
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Abstract
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In this paper, we present two constructions of QLTCs with constant soundness. In the first approach, we introduce an operation which we call check product, and show how this operation gives rise to QLTCs of constant soundness, constant rate, and distance scaling with locality. In the second approach, we utilize homological product of codes and prove a special case in which the soundness of component codes is preserved through the homological product. This observation leads us to construct QLTCs of constant soundness, scalable rate and distance, and constant average locality. Our work marks a step towards constructing QLTCs of high soundness and distance, which would give a different construction to the No Low-Energy Trivial States (NLTS) theorem.