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In this paper, we employ PCA and t-SNE analysis to gain deeper insights intothe behavior of entangled and non-entangled mixing operators within the QuantumApproximate Optimization Algorithm (QAOA) at varying depths. Our study utilizesa dataset of parameters generated for max-cut problems using the StochasticHill Climbing with Random Restarts optimization method in QAOA. Specifically,we examine the $RZ$, $RX$, and $RY$ parameters within QAOA models at depths of$1L$, $2L$, and $3L$, both with and without an entanglement stage inside themixing operator. The results reveal distinct behaviors when we process thefinal parameters of each set of experiments with PCA and t-SNE, where inparticular, entangled QAOA models with $2L$ and $3L$ present an increase in theamount of information that can be preserved in the mapping. Furthermore,certain entangled QAOA graphs exhibit clustering effects in both PCA and t-SNE.Overall, the mapping results clearly demonstrate a discernible differencebetween entangled and non-entangled models, quantified numerically throughexplained variance in PCA and Kullback-Leibler divergence (after optimization)in t-SNE, where some of these differences are also visually evident in themapping data produced by both methods.

PCA and t-SNE analysis in the study of QAOA entangled and non-entangled mixing operators