Retrieving non-stabilizerness with Neural Networks

Abstract: Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic) states. Despite their significance, quantifying and characterizing these states pose formidable challenges. Here, we introduce a novel approach leveraging Convolutional Neural Networks (CNNs) to classify quantum states based on their magic content. Without relying on a complete knowledge of the state, we utilize partial information acquired from measurement snapshots to train the CNN in distinguishing between stabilizer and nonstabilizer states. Importantly, our methodology circumvents the limitations of full state tomography, offering a practical solution for real-world quantum experiments. In addition, we unveil a theoretical connection between Stabilizer R\'enyi Entropies (SREs) and the expectation value of Pauli matrices for pure quantum states. Our findings pave the way for experimental applications, providing a robust and accessible tool for deciphering the intricate landscape of quantum resources.