Resource-efficient quantum correlation measurements via multicopy neural network methods

Measuring complex properties in quantum systems, such as measures of quantum entanglement and Bell nonlocality, is inherently challenging. Traditional methods, like quantum state tomography (QST), require a full reconstruction of the density matrix for a given system and demand resources that scale exponentially with system size. We propose an alternative strategy that reduces the required information by combining multicopy measurements with artificial neural networks (ANNs), resulting in a 67% reduction in measurement requirements compared to QST. We have successfully measured two-qubit quantum correlations of Bell states subjected to a depolarizing channel (resulting in Werner states) and an amplitude-damping channel (leading to Horodecki states) using the multicopy approach on real quantum hardware. Our experiments, conducted with transmon qubits on IBMQ quantum processors, quantified the violation of Bell's inequality and the negativity of two-qubit entangled states. We compared these results with those obtained from the standard QST approach and applied a maximum likelihood method to mitigate noise. We trained ANNs to estimate degrees of entanglement and nonlocality measures using optimized sets of projections identified through Shapley's (SHAP) analysis for the Werner and Horodecki states. The ANN output, based on this reduced set of projections, aligns well with expected values and enhances noise robustness. This approach simplifies and improves the error robustness of multicopy measurements, eliminating the need for complex nonlinear equation analysis. It represents a significant advancement in AI-assisted quantum measurements, making the practical implementation on current quantum hardware more feasible. The experimental results demonstrate improved noise robustness on the current noisy intermediate-scale quantum (NISQ) hardware, representing a practical advance in resource-efficient characterization of quantum correlations.