Non-maximum suppression (NMS) has been adopted by default for removing redundant object detections for decades. It eliminates false positives by only keeping the image M with highest detection score and images whose overlap ratio with M is less than a predefined threshold. However, this greedy algorithm may not work well for object detection under occlusion scenario where true positives with lower detection scores are possibly suppressed. In this paper, we first map the task of removing redundant detections into Quadratic Unconstrained Binary Optimization (QUBO) framework that consists of detection score from each bounding box and overlap ratio between pair of bounding boxes. Next, we solve the QUBO problem using the proposed Quantum-soft QUBO Suppression (QSQS) algorithm for fast and accurate detection by exploiting quantum computing advantages. Experiments indicate that QSQS improves mean average precision from 74.20% to 75.11% for PASCAL VOC 2007. It consistently outperforms NMS and soft-NMS for Reasonable subset of benchmark pedestrian detection CityPersons.