The ab initio calculation of exact quantum reaction rate constants comes at a high cost due to the required dynamics of reactants on multidimensional potential energy surfaces. In turn, this impedes the rapid design of the kinetics for large sets of coupled reactions. In an effort to overcome this hurdle, a deep neural network (DNN) was trained to predict the logarithm of quantum reaction rate constants multiplied by their reactant partition function-rate products. The training dataset was generated in-house and contains similar to 1.5 million quantum reaction rate constants for single, double, symmetric and asymmetric one-dimensional potentials computed over a broad range of reactant masses and temperatures. The DNN was able to predict the logarithm of the rate product with a relative error of 1.1%. Furthermore, when comparing the difference between the DNN prediction and classical transition state theory at temperatures below 300 K a relative percent error of 31% was found with respect to the exact difference. Systems beyond the test set were also studied, these included the H + H-2 reaction, the diffusion of hydrogen on Ni(100), the Menshutkin reaction of pyridine with CH3Br in the gas phase, the reaction of formalcyanohydrin with HS- in water and the F + HCl reaction. For these reactions, the DNN predictions were accurate at high temperatures and in good agreement with the exact rates at lower temperatures. This work shows that one can take advantage of a DNN to gain insight on reactivity in the quantum regime.