# Optimization Strategies in Quantum Machine Learning: A Performance Analysis
## 5 Comparative Analysis
### ADAM Optimizer
Recall (Sensitivity): Recall evaluates a model's ability to identify all actual positive instances. Both COBYLA and ADAM achieved a recall rate of 97%, showcasing their efficiency in minimizing false negatives. L-BFGS-B trailed slightly with a recall of 94%, which, while still strong, suggests a marginally higher tendency to miss positive cases. 4. F1 Score: F1 score provides a balanced measure of precision and recall, offering insight into the overall effectiveness of a model. COBYLA achieved the highest F1 score of 93%, reflecting its superior ability to balance these two critical metrics. L-BFGS-B exhibited an F1 score of 90%, indicating a good performance but falling short of COBYLA's optimization capabilities. ADAM achieved the lowest value of 68% on the F1 score. 5. Convergence: The performance of the optimizers reveals distinct differences in loss, despite all three--L-BFGS-B, COBYLA, and ADAM--achieving 100% convergence. 6. Loss: COBYLA demonstrated the lowest loss at 8.20%, indicating superior optimization in this context. L-BFGS-B resulted in a loss of 11.48%, which is notably higher than COBYLA's. In contrast, ADAM exhibited a significantly elevated loss of 47.54%. Discussion  
* COBYLA consistently outperformed the other optimizers across all metrics, achieving the highest accuracy (92%), precision (89%), and F1 score (93%). Its recall rate of 97%, tied with ADAM's, indicates a good ability to minimize false negatives. Additionally, achieving the minimum loss in just 1 min of training, COBYLA is the most computationally efficient optimizer, solidifying its position as the optimal choice for this model. * L-BFGS-B demonstrated moderate performance, with accuracy (89%) and recall (94%) values slightly lower than COBYLA's. While it achieved a precision of 86%, its overall F1 score (90%) indicated balanced but less effective performance compared to COBYLA. Its training time of 6 min was longer than COBYLA's, though still reasonable. Additionally, the loss for L-BFGS-B was 11.48%, indicating a less effective optimization compared to COBYLA's loss but significantly better than ADAM's loss. * ADAM's performance was notably weaker, particularly in terms of accuracy (52%) and precision (53%). Despite achieving a high recall rate of 97%, comparable to COBYLA's, its poor precision resulted in an imbalanced model, as reflected in the F1 score of 68%. This pattern, characterized by high recall at the expense of precision,often indicates a strong bias towards predicting the positive class, where the model effectively captures most actual positives but incurs a significant number of false positives, ultimately leading to suboptimal overall accuracy. Furthermore, ADAM exhibited the longest training time of 10 min among the three optimizers, rendering it the least efficient choice in this context. Adding to its poor performance, ADAM demonstrated a significantly higher loss of 47.54%, indicating a substantial discrepancy between predicted and actual outcomes compared to both COBYLA's 8.20% and L-BFGS-B's 11.48% loss. Although all optimizers achieved convergence (100%), the significant disparity in their final loss underscores the critical impact of optimizer selection in quantum machine learning models, necessitating choices tailored to this domain. Consistent with findings in prior work by [PERSON] et al. [47], which demonstrated COBYLA's strong performance and ability to achieve low cost values in noise-free simulations, COBYLA's observed efficiency in our study reinforces its potential as a benchmark for similar quantum learning tasks.