Distributed Denial of Service (DDoS) attacks pose a significant threat to the security of networking systems, as they can cause widespread disruption and even bring down entire distributed systems platforms. In this paper, we propose an approach called the DEQSVC that leverages quantum machine learning techniques to detect DDoS attacks with high accuracy. The DEQSVC integrates the most efficient dimensionality reduction techniques, a robust feature map method, and an efficient kernel estimation technique to improve data encoding, learning process, and detection accuracy. To evaluate the performance of the proposed DEQSVC, we conducted simulations using the Qiskit platform and executed the approach on an IBM quantum computer. Our results demonstrate that the DEQSVC outperforms several benchmark algorithms commonly used in intrusion detection systems. Specifically, the DEQSVC achieves a detection accuracy of 99.49, indicating its effectiveness as a highly accurate and efficient method for detecting DDoS attacks.