Segmenting stroke lesions and assessing the thrombolysis in cerebral infarction (TICI) grade are two important but challenging prerequisites for an auxiliary diagnosis of the stroke. However, most previous studies have focused only on a single one of two tasks, without considering the relation between them. In our study, we propose a simulated quantum mechanics-based joint learning network (SQMLP-net) that simultaneously segments a stroke lesion and assesses the TICI grade. The correlation and heterogeneity between the two tasks are tackled with a single-input double-output hybrid network. SQMLP-net has a segmentation branch and a classification branch. These two branches share an encoder, which extracts and shares the spatial and global semantic information for the segmentation and classification tasks. Both tasks are optimized by a novel joint loss function that learns the intra- and inter-task weights between these two tasks. Finally, we evaluate SQMLP-net with a public stroke dataset (ATLAS R2.0). SQMLP-net obtains state-of-the-art metrics (Dice:70.98% and accuracy:86.78%) and outperforms single-task and existing advanced methods. An analysis found a negative correlation between the severity of TICI grading and the accuracy of stroke lesion segmentation.