In this paper, the author establishes the regularity properties of the cubic biharmonic nonlinear Schrödinger equations on the half line $$ iu_t + \partial^4_x u \pm|u|^2u = 0, \ x \in \Bbb R^+,\ t\in\Bbb R^+. $$ He uses Laplace transform methods proposed by J.~L. Bona, S.-M. Sun and B.-Y. Zhang [J. Math. Pures Appl. (9) {\bf 109} (2018), 1--66; MR3734975] to divide the problem into a linear IBVP on the half line and nonlinear IVP on the full line after extending the data into $\Bbb R$. By the $X^{s,b}$ method [J. Bourgain, Geom. Funct. Anal. {\bf 3} (1993), no.~3, 209--262; MR1215780], the author proves that the nonlinear part of the solution is smoother than the initial data, then he obtains a smoothing result in the low-regularity spaces on the half line by adapting the estimates of M.~B. Erdoğan and N. Tzirakis [J. Funct. Anal. {\bf 271} (2016), no.~9, 2539--2568; MR3545224]. The local well-posedness theory is established via the contraction argument. Moreover, in the defocusing case, he establishes global well-posedness and global smoothing in the higher order regularity spaces.