In this study, we use cross-domain classification using quantum machine learning for quantum advantages to address the entanglement versus separability paradigm. We further demonstrate the efficient classification of Bell diagonal states into zero and non-zero discord classes. The inherited structure of quantum states and its relation with a particular class of quantum states are exploited to intuitively approach the classification of different domain testing states, referred here as crossdomain classification. In addition, we extend our analysis to evaluate the robustness of our model for the analyzed problem using random unitary transformations. Using numerical analysis, our results clearly demonstrate the potential of QSVM for classifying quantum states across the multidimensional Hilbert space.

Here, we use the nomenclature derived from the meta-learning literature which is the most prevalent at time of writing. Let S {( x l,y l)} L l 1 be a support-set containing input-output pairs, with L equal to one (1-shot) or five (5-shot), and Q { (x m,y m)} M m 1be a query-set (sometimes referred to in the literature as a target-set), with M typically one order of magnitude greater than L. For ease of notation, the support and query sets are grouped in a task T {S, Q}, with the dataset D {T n} N n 1 defined as a collection of such tasks. Models are trained on random tasks sampled from D . Then, given a new task T {S, Q } sampled from a test set, the objective is to condition the model on the samples of the support S to estimate the membership of the samples in the query set Q . In the most common scenario, the inputs x D belong to the same distribution p(x) and are distributed across training, validation, and test sets such that their class membership is non-overlapping. Note that y can be a continuous value (regression) or a discrete one (classification), even though most of the previous work has focused on classification. We also consider the cross-domain scenario, where the inputs are sampled from different distributions at training and test time; this is more representative of real-world scenarios.