A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification
Abstract
:1. Introduction
2. The Construction of the Classifier
2.1. Convex Hull Approximation
2.2. A Tangent-Based Classifier via CHA
2.2.1. Voronoi Diagram
2.2.2. Minimum Hyper-Body
2.3. Combining CHA and Machine Learning
2.3.1. Data Preparation
2.3.2. Extended Data Form
2.3.3. Ensemble Learning
3. The Performance of the Classifier
3.1. Training Phase of the Predictors
3.2. Testing Phase of the Predictors
3.2.1. Algorithm for Calculating the
- (1)
- Randomly sample a state from a uniform distribution according to the Haar measure;
- (2)
- Randomly sample a state from a uniform distribution according to the Haar measure;
- (3)
- Return .
3.2.2. Algorithm for Finding Critical Points
- (1)
- Initiate p as the feature vector of , and set ;
- (2)
- Update ;
- (3)
- Now, . Pick to be the critical points satisfying . Update ;
- (4)
- For each , suppose is the feature vector of . Sample the neighbor of ; that is, to randomly generate two Hermitian operators , satisfying . Let be a random number in . Set . Set , where is the feature vector of ;
- (5)
- Update and go back to step 2.
3.2.3. Algorithm for Calculating an Approximate Tangent Hyperplane
- (1)
- Divide the n critical points into 50 parts, each of which contains m critical points. Generate a Voronoi diagram via each part. Here, we directly implement the function voronoin.m of the Qhull toolbox [30] to generate the n-dimensional Voronoi diagram.
- (2)
- Find the minimum hyper-body via the adjacent target points. Generate the corresponding tangent hyperplane. Decide which states are GHZ states according to the hyperplane.
- (3)
- Repeat step 2 50 times or until all the diagrams have been used.
4. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Method | SVM | Decision Tree | Bagging | Boosting |
---|---|---|---|---|
Error (%) | 14.1 | 25.2 | 18.8 | 17.3 |
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Wang, P. A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification. Appl. Sci. 2022, 12, 12778. https://doi.org/10.3390/app122412778
Wang P. A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification. Applied Sciences. 2022; 12(24):12778. https://doi.org/10.3390/app122412778
Chicago/Turabian StyleWang, Pingxun. 2022. "A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification" Applied Sciences 12, no. 24: 12778. https://doi.org/10.3390/app122412778
APA StyleWang, P. (2022). A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification. Applied Sciences, 12(24), 12778. https://doi.org/10.3390/app122412778