In light of the growing proportion of older individuals in our society, the timely diagnosis of Alzheimer's disease has become a crucial aspect of healthcare. In this paper, we propose a non-invasive and cost-effective detection method based on speech technology. The method employs a pre-trained language model in conjunction with techniques such as prompt fine-tuning and conditional learning, thereby enhancing the accuracy and efficiency of the detection process. To address the issue of limited computational resources, this study employs the efficient LORA fine-tuning method to construct the classification model. Following multiple rounds of training and rigorous 10-fold cross-validation, the prompt fine-tuning strategy based on the LLAMA2 model demonstrated an accuracy of 81.31\%, representing a 4.46\% improvement over the control group employing the BERT model. This study offers a novel technical approach for the early diagnosis of Alzheimer's disease and provides valuable insights into model optimization and resource utilization under similar conditions. It is anticipated that this method will prove beneficial in clinical practice and applied research, facilitating more accurate and efficient screening and diagnosis of Alzheimer's disease.