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In this work, we propose an improved method of training linear support vectormachines (SVMs) to generate entanglement witnesses for systems of 3, 4, and 5qubits. SVMs generate hyperplanes represented by a weighted sum of expectationvalues of local observables, whose coefficients are optimized to provide apositive sum for all separable states and a negative sum for as many entangledstates as possible near a specific target state. We use the eigenstates ofgeneralized Pauli matrices as training data, and correct the witnesses with adifferential program. This method requires only $ O(6^n)$ training states,whereas an existing method needs$ O(2^{4^n})$. We use this method to constructwitnesses of 4 and 5 qubit GHZ states with coefficients agreeing withstabilizer formalism witnesses to within 6.5 percent and 1 percent,respectively. We also use the same training states to generate 4 and 5 qubit Wstate witnesses. Finally, we propose methods for physical and computationalverification of these witnesses.

An Exponential Reduction in Training Data Sizes for Machine Learning Derived Entanglement Witnesses