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This work proposes QNet, a novel sequence encoder model that entirely inferences on the quantum computer using a minimum number of qubits. Let $n$ and $d$ represent the length of the sequence and the embedding size, respectively. The dot-product attention mechanism requires a time complexity of $O(n^2 \cdot d)$, while QNet has merely $O(n+d)$ quantum circuit depth. In addition, we introduce ResQNet, a quantum-classical hybrid model composed of several QNet blocks linked by residual connections, as an isomorph Transformer Encoder. We evaluated our work on various natural language processing tasks, including text classification, rating score prediction, and named entity recognition. Our models exhibit compelling performance over classical state-of-the-art models with a thousand times fewer parameters. In summary, this work investigates the advantage of machine learning on near-term quantum computers in sequential data by experimenting with natural language processing tasks.