  In our previous paper we derived the holographic dual of the planar fishnet
CFT in four dimensions. The dual model becomes classical in the strongly
coupled regime of the CFT and takes the form of an integrable chain of
particles in five dimensions. Here we study the theory at the quantum level. By
applying the canonical quantization procedure with constraints, we show that
the model describes a quantum chain of particles propagating in $AdS_5$. We
prove the duality at the full quantum level in the ${\mathfrak u}(1)$ sector
and reproduce exactly the spectrum for the cases when it is known analytically.
