Network quantization is an effective compression method to reduce the model size and computational cost. Despite the high compression ratio, training a low-precision model is difficult due to the discrete and non-differentiable nature of quantization, resulting in considerable performance degradation. Recently, Sharpness-Aware Minimization (SAM) is proposed to improve the generalization performance of the models by simultaneously minimizing the loss value and the loss curvature. In this paper, we devise a Sharpness-Aware Quantization (SAQ) method to train quantized models, leading to better generalization performance. Moreover, since each layer contributes differently to the loss value and the loss sharpness of a network, we further devise an effective method that learns a configuration generator to automatically determine the bitwidth configurations of each layer, encouraging lower bits for flat regions and vice versa for sharp landscapes, while simultaneously promoting the flatness of minima to enable more aggressive quantization. Extensive experiments on CIFAR-100 and ImageNet show the superior performance of the proposed methods. For example, our quantized ResNet-18 with 55.1x Bit-Operation (BOP) reduction even outperforms the full-precision one by 0.7% in terms of the Top-1 accuracy. Code is available at this https URL.