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Quantum devices with low qubits are common in the Noisy Intermediate-Scale Quantum (NISQ) era. However, Quantum Neural Network (QNN) running on low-qubit quantum devices would be difficult since it is based on Variational Quantum Circuit (VQC), which requires many qubits. Therefore, it is critical to make QNN with VQC run on low-qubit quantum devices. In this study, we propose a novel VQC called the low-qubit VQC. VQC requires numerous qubits based on the input dimension; however, the low-qubit VQC with linear transformation can liberate this condition. Thus, it allows the QNN to run on low-qubit quantum devices for speech applications. Furthermore, as compared to the VQC, our proposed low-qubit VQC can stabilize the training process more. Based on the low-qubit VQC, we implement QSpeech, a library for quick prototyping of hybrid quantum-classical neural networks in the speech field. It has numerous quantum neural layers and QNN models for speech applications. Experiments on Speech Command Recognition and Text-to-Speech show that our proposed low-qubit VQC outperforms VQC and is more stable.