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

• URL: http://arxiv.org/abs/2306.11060v1
• Date: Mon, 19 Jun 2023 16:50:32 GMT
• Title: PCA and t-SNE analysis in the study of QAOA entangled and non-entangled mixing operators
• Authors: Brian Garc\'ia Sarmina, Guo-Hua Sun and Shi-Hai Dong
• Abstract summary: We employ PCA and t-SNE analysis to gain deeper insights into the behavior of entangled and non-entangled mixing operators. Specifically, we examine the $RZ$, $RX$, and $RY$ parameters within QAOA models at depths of $1L$, $2L$, and $3L$. The results reveal distinct behaviors when we process the final parameters of each set of experiments with PCA and t-SNE, where in particular, entangled QAOA models with $2L$ and $3L$ present an increase in the amount of information that can be preserved in the mapping
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we employ PCA and t-SNE analysis to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at varying depths. Our study utilizes a dataset of parameters generated for max-cut problems using the Stochastic Hill 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 the mixing operator. The results reveal distinct behaviors when we process the final parameters of each set of experiments with PCA and t-SNE, where in particular, entangled QAOA models with $2L$ and $3L$ present an increase in the amount 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 difference between entangled and non-entangled models, quantified numerically through explained variance in PCA and Kullback-Leibler divergence (after optimization) in t-SNE, where some of these differences are also visually evident in the mapping data produced by both methods.

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