To support multiple transmissions in an optical fiber, several techniques have been studied such as Optical Code Division Multiple Access (OCDMA). In particular, the incoherent OCDMA systems are appreciated for their simplicity and reduced cost. However, they suffer from Multiple Access Interference (MAI), which degrades the performances. In order to cope with this MAI, several detectors have been studied. Among them, the Maximum Likelihood (ML) detector is the optimal one but it suffers from high complexity as all possibilities have to be tested prior to decision. However, thanks to the recent quantum computing advances, the complexity problem can be circumvented. Indeed, quantum algorithms, such as Grover, exploit the superposition states in the quantum domain to accelerate the computation. Thus, in this paper, we propose to adapt the quantum Grover's algorithm in the context of MUD, in an OCDMA system using non-orthogonal codes. We propose a way to adapt the received noisy signal to the constraints defined by Grover's algorithm. We further evaluate the probability of success in detecting the active users for different noise levels. Aside from the complexity reduction, simulations show that our proposal has a high probability of detection when the received signal is not highly altered. We show the benefits of our proposal compared to the classical and the optimal ML detector.