Machine Learning-Derived Entanglement Witnesses

Recent studies of the classification of entangled states have utilized aspects of machine learning such as neural networks. However, the number of features (or observables) taken as input into such systems required to provide correct inference often grow to the number required for full state tomography.

Here, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target states.

An SVM allows for the construction of a hyperplane that clearly delineates between separable states and the target state; this hyperplane is essentially a weighted sum of observables (‘features’) whose weights are adjusted during the training of the SVM. In contrast to other methods such as deep neural nets, the training of an SVM is a convex optimization problem and results in an ‘optimal’ solution every time. We show that SVMs are flexible enough to allow us to rank features, and to reduce the number of features systematically while bounding the inference error. This programmatic approach will allow us to streamline the detection of entangled states in experiment.