Quantification of entanglement with Siamese convolutional neural networks

Quantum entanglement is a fundamental property commonly used in various quantum information protocols and algorithms. Nonetheless, the problem of quantifying entanglement has still not reached general solution for systems larger than two qubits. In this paper, we investigate the possibility of detecting entanglement with the use of the supervised machine learning method, namely the deep convolutional neural networks. We build a model consisting of convolutional layers, which is able to recognize and predict the presence of entanglement for any bipartition of the given multi-qubit system. We demonstrate that training our model on synthetically generated datasets collecting random density matrices, which either include or exclude challenging positive-under-partial-transposition entangled states (PPTES), leads to the different accuracy of the model and its possibility to detect such states. Moreover, it is shown that enforcing entanglement-preserving symmetry operations (local operations on qubit or permutations of qubits) by using triple Siamese network, can significantly increase the model performance and ability to generalize on types of states not seen during the training stage. We perform numerical calculations for 3,4 and 5-qubit systems, therefore proving the scalability of the proposed approach.