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We prove the local well-posedness of the initial boundary value problem forthe nonlinear quadratic Schr\"odinger equation under low initial-boundaryregularity assumption via the boundary integral operator method introduced byBona-Sun-Zhang (Trans. Amer. Math. Soc., 354(2):427-490, 2002).

A lower index bilinear estimate for the quadratic Schr\"odinger equation and application for its half line problem