  We consider a cusped Wilson line with J insertions of scalar fields in N=4
SYM and prove that in a certain limit the Feynman graphs are integrable to all
loop orders. We identify the integrable system as a quantum fishchain with open
boundary conditions. The existence of the boundary degrees of freedom results
in the boundary reflection operator acting non-trivially on the physical space.
We derive the Baxter equation for Q-functions and provide the quantisation
condition for the spectrum. This allows us to find the non-perturbative
spectrum numerically.
