Teacher-Student Learning for a Binary Perceptron with Quantum Fluctuations

We analyse 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 the binary perceptron. In this study, we consider the teacher-student learning and compute the generalisation error of the binary perceptron with quantum fluctuations. Due to quantum fluctuations, we can efficiently find robust solutions that have better generalisation performance than the classical model. We validate our theoretical results through quantum Monte Carlo simulations. We adopt the replica symmetry (RS) ansatz and static approximation. The RS solutions are consistent with our numerical 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.