  The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type
IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling
using integrability. Starting from the results of [arXiv:1403.1859], we study
in depth the basic integrability structure underlying the spectral problem, the
Quantum Spectral Curve. The new results presented in this paper open the way to
the quantitative study of the spectrum for arbitrary operators at finite
coupling. Besides, we show that the Quantum Spectral Curve is embedded into a
novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and
leads to exact Bethe Ansatz equations. The discovery of this algebraic
structure, more intricate than the one appearing in the $AdS_5/CFT_4$ case,
could be a first step towards the extension of the method to $AdS_3/CFT_2$.
