  In this paper, we present two constructions of quantum locally testable codes
(QLTC) with constant soundness. In the first approach, we introduce an
operation called 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 consider hypergraph product of a quantum code and a
classical repetition code, and observe a special case in which the soundness of
component codes is preserved. This insight 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.
