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We develop in a companion article the kinematics of three-dimensional loopquantum gravity in Euclidean signature and with a negative cosmologicalconstant, focusing in particular on the spinorial representation which iswell-known at zero cosmological constant. In this article, we put thisformalism to the test by quantizing the Hamiltonian constraint on the dual of atriangulation. The Hamiltonian constraints are obtained by projecting theflatness constraints onto spinors, as done in the flat case by the first authorand Livine. Quantization then relies on $q$-deformed spinors. The quantumHamiltonian constraint acts in the $q$-deformed spin network basis asdifference equations on physical states, which are thus the Wheeler-DeWittequations in this framework. Moreover, we study how physical states transformunder Pachner moves of the canonical surface. We find that thosetransformations are in fact $q$-deformations of the transition amplitudes ofthe flat case as found by Noui and Perez. Our quantum Hamiltonian constraintstherefore build a Turaev-Viro model at real $q$.

Spinor Representation of the Hamiltonian Constraint in 3D LQG with a Non-zero Cosmological Constant