Active user detection in a non-orthogonal multiple access (NOMA) network is a major challenge for 5G/6G applications. However, classical algorithms that can perform this task suffer either from complexity or reduced performances. This work aims at proposing a quantum annealing approach to overcome this trade-off. Firstly, we show that the maximum a posteriori decoder of the activity pattern of the network can be seen as the ground state of an Ising Hamiltonian. For N users in a network with perfect channels, we propose a universal control function to schedule the annealing process. Our approach avoids to continuously compute the optimal control function but still ensures high success probability while demanding a lower annealing time than a linear control function. This advantage holds even in the presence of imperfections in the network.