Pseudo quantum advantages in perceptron storage capacity

We investigate a generalized quantum perceptron architecture characterized by an oscillating activation function with a tunable frequency ranging from zero to infinity. Employing analytical techniques from statistical mechanics, we derive the optimal storage capacity and demonstrate that the classical result is recovered in the limit of vanishing frequency. As the frequency increases, however, the architecture exhibits enhanced quantum storage capabilities. Notably, this improvement stems solely from the specific form of the activation function and, in principle, could be emulated within a classical framework. Accordingly, we refer to this enhancement as a pseudo quantum advantage.