Pseudo quantum advantages in perceptron storage capacity
Fabio Benatti, Masoud Gharahi, Giovanni Gramegna, Stefano Mancini, Vincenzo Parisi
TL;DR
This work analyzes the storage capacity of a generalized quantum perceptron with an oscillating activation function controlled by a frequency parameter $\lambda$. Using Gardner’s framework and the replica trick, it shows that the classical capacity $\alpha_c(0)=2$ is recovered at $\lambda\to 0$, while increasing $\lambda$ yields a capacity $\alpha_c(\lambda)$ that can grow without bound, signaling a pseudo quantum advantage arising from the activation function rather than true quantum computation. The improvement can, in principle, be emulated within a classical setup, casting doubt on a genuine quantum advantage for a single perceptron; the authors highlight that a genuine quantum edge may emerge in networks of interacting quantum perceptrons. The results establish a bridge between classical storage theory and quantum perceptron models, and point to future directions exploring generalization behavior and possible replica-symmetry breaking in more complex quantum neural architectures. Overall, the paper clarifies how activation-form-induced nonlinearities can modulate storage capacity and cautions against conflating such effects with true quantum computational power.
Abstract
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.