Sentiment analysis finds widespread applications in health, marketing, finance, stock markets, media, and politics. To analyze attitudes and emotions in textual data, handling large datasets and significant computational power is essential. Traditional computing methods struggle with the growing data volume, prompting interest in quantum computing as a promising alternative with its inherent high-speed processing capacity. This study focuses on sentiment analysis applied to texts derived from bilateral conversation dialogues. The primary objective is to categorize emotions within the text as positive, neutral, or negative, while concurrently identifying the speaker. To achieve this, a novel quantum-classical hybrid approach is proposed. The quantum side of this approach includes the variational quantum circuit (VQC). On the classical side, preprocessing of the data set, feature extraction with a model containing LSTM, and optimizing the parameters of VQC are performed. The proposed approach was trained and tested using a data set containing bilateral conversations. As a result of the tests, the proposed approach achieved a higher accuracy rate compared to studies using the classical approach. Thus, the effectiveness of the proposed approach is confirmed.