Simulating Nonlinearity in Quantum Neural Networks While Mitigating Barren Plateaus

Abstract: Quantum neural networks (QNNs) encounter significant challenges in realizing nonlinear behavior and effectively optimizing parameters. This study addresses these issues by modeling nonlinearity through a Taylor series expansion, where the method uses tensor products to generate the series basis, and parameterized unitary matrices define the corresponding coefficients. This design substantially reduces quantum circuit depth compared to conventional methods that rely on parameterized quantum gates, thereby mitigating the barren plateau problem. A QNN was implemented and tested on the MNIST and Fashion MNIST datasets to evaluate the proposed method, achieving test accuracies of 98.7% and 88.3%, respectively. With noise added, the accuracy decreased slightly to 98.6% and 87.2%.