PCA and t-SNE analysis in the study of QAOA entangled and non-entangled mixing operators
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arXiv
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| Natura: | Preprint |
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2023
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| author | Sarmina, Brian García Sun, Guo-Hua Dong, Shi-Hai |
| author_facet | Sarmina, Brian García Sun, Guo-Hua Dong, Shi-Hai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11060 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | PCA and t-SNE analysis in the study of QAOA entangled and non-entangled mixing operators Sarmina, Brian García Sun, Guo-Hua Dong, Shi-Hai Quantum Physics 81P68, 68Q09, 68Q12 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. |
| title | PCA and t-SNE analysis in the study of QAOA entangled and non-entangled mixing operators |
| topic | Quantum Physics 81P68, 68Q09, 68Q12 |
| url | https://arxiv.org/abs/2306.11060 |