The roles of Kerr nonlinearity in a bosonic quantum neural network

Abstract

The emerging technology of quantum neural networks (QNNs) offers a quantum advantage over classical artificial neural networks (ANNs) in terms of speed or efficiency of information processing tasks. It is well established that nonlinear mapping between input and output is an indispensable feature of classical ANNs, while in a QNN the roles of nonlinearity are not yet fully understood. As one tends to think of QNNs as physical systems, it is natural to think of nonlinear mapping originating from a physical nonlinearity of the system, such as Kerr nonlinearity. Here we investigate the effect of Kerr nonlinearity on a bosonic QNN in the context of both classical (simulating an XOR gate) and quantum (generating Schrödinger cat states) tasks. Aside offering a mechanism of nonlinear input-output mapping, Kerr nonlinearity reduces the effect of noise or losses, which are particularly important to consider in the quantum setting. We note that nonlinear mapping may also be introduced through a nonlinear input-output encoding rather than a physical nonlinearity: for example, an output intensity is already a nonlinear function of input amplitude. While in such cases Kerr nonlinearity is not strictly necessary, it still increases the performance in the face of noise or losses.