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- Title
Principal Component Analysis and t-Distributed Stochastic Neighbor Embedding Analysis in the Study of Quantum Approximate Optimization Algorithm Entangled and Non-Entangled Mixing Operators.
- Authors
Sarmina, Brian García; Sun, Guo-Hua; Dong, Shi-Hai
- Abstract
In this paper, we employ PCA and t-SNE analyses to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at various depths. We utilize a dataset containing optimized parameters generated for max-cut problems with cyclic and complete configurations. This dataset encompasses the resulting R Z , R X , and R Y parameters for QAOA models at different depths ( 1 L , 2 L , and 3 L ) with or without an entanglement stage within the mixing operator. Our findings reveal distinct behaviors when processing the different parameters with PCA and t-SNE. Specifically, most of the entangled QAOA models demonstrate an enhanced capacity to preserve information in the mapping, along with a greater level of correlated information detectable by PCA and t-SNE. Analyzing the overall mapping results, a clear differentiation emerges between entangled and non-entangled models. This distinction is quantified numerically through explained variance in PCA and Kullback–Leibler divergence (post-optimization) in t-SNE. These disparities are also visually evident in the mapping data produced by both methods, with certain entangled QAOA models displaying clustering effects in both visualization techniques.
- Subjects
OPTIMIZATION algorithms; STOCHASTIC analysis; PRINCIPAL components analysis; QUANTUM operators; DATA mapping; QUANTUM information theory
- Publication
Entropy, 2023, Vol 25, Issue 11, p1499
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e25111499