  We analysed the generalisation performance of a binary perceptron with
quantum fluctuations using the replica method. An exponential number of local
minima dominate the energy landscape of the binary perceptron. Local search
algorithms often fail to identify the ground state of a binary perceptron. In
this study, we considered the teacher-student learning method and computed the
generalisation error of a binary perceptron with quantum fluctuations. Due to
the quantum fluctuations, we can efficiently find robust solutions that have
better generalisation performance than the classical model. We validated our
theoretical results through quantum Monte Carlo simulations. We adopted the
replica symmetry (RS) ansatz assumption and static approximation. The RS
solutions are consistent with our simulation results, except for the relatively
low strength of the transverse field and high pattern ratio. These deviations
are caused by the violation of ergodicity and static approximation. After
accounting for the deviation between the RS solutions and numerical results,
the enhancement of generalisation performance with quantum fluctuations holds.
