Introduction Quantum Convolutional Neural Network (QCNN)-Long Short-Term Memory (LSTM) models were studied to provide sequential relationships for each timepoint in MRIs of patients with Multiple Sclerosis (MS). In this pilot study, we compared three QCNN-LSTM models for binary classification of MS disability benchmarked against classical neural network architectures. Our hypothesis is that quantum models will provide competitive performance. Methods Matrix Product State (MPS), reverse Multistate Entanglement Renormalization Ansatz (MERA), and Tree-Tensor Network (TTN) circuits were paired with LSTM layer to process near-annual MRI data of patients diagnosed with MS. These were benchmarked against a Visual Geometry Group (VGG)-LSTM and a Video Vision Transformer (ViViT). Predicted logits were measured against ground truth labels of each patient's Extended Disability Severity Score (EDSS) using binary cross-entropy loss. Training/validation/holdout testing was partitioned using 5-fold cross validation with a total split of 60:20:20. Levene's test of variance was used to measure statistical difference and Student's t-test for paired model differences in mean. Results The MPS-LSTM, reverse MERA-LSTM, and TTN-LSTM had holdout testing ROC-AUC of 0.70, 0.77, and 0.81, respectively (p-value 0.915). VGG16-LSTM and ViViT performed similarly with ROC-AUC of 0.73 and 0.77, respectively (p-value 0.631). Overall variance and mean were not statistically significant (p-value 0.713), however, time to train was significantly faster for the QCNN-LSTMs (39.4 sec per fold vs. 224 and 218, respectively, p-value <0.001). Conclusion QCNN-LSTM models perform competitively to their classical counterparts with greater efficiency in train time. Clinically, these can add value in terms of efficiency to time-dependent deep learning prediction of disease progression based upon medical imaging.