The development of energy-efficient neural network hardware using magnetic tunnel junction (MTJ) devices has been widely investigated. One of the issues in the use of MTJ devices is large write energy. Since MTJ devices show stochastic behaviors, a large write current with enough time length is required to guarantee the certainty of the information held in MTJ devices. This paper demonstrates that quantized neural networks (QNNs) exhibit high tolerance to bit errors in weights and an output feature map. Since probabilistic switching errors in MTJ devices do not have always a serious effect on the performance of QNNs, large write energy is not required for reliable switching operations of MTJ devices. Based on the evaluation results, we achieve about 80% write-energy reduction on buffer memory compared to the conventional method. In addition, it is demonstrated that binary representation exhibits higher bit-error tolerance than the other data representations in the range of large error rates.