Quantum metric learning with fuzzy-informed learning

By constructing a quantum circuit with adjustable parameters, variational quantum circuits are capable of embedding input data into Hilbert space and facilitating the execution of complex deep learning tasks. Recently, a method known as quantum metric learning has emerged. It adaptively adjusts quantum embedding circuits to enable clusters of classical data from different categories to form linear separations in Hilbert space. This approach combines the advantages of kernel methods and is implementable on near-term quantum devices. However, applying quantum metric learning to more complex data presents challenges, largely due to the inherent fuzziness, uncertainty, and noise in the data itself and in the classical neural network preprocessing. To address these challenges, this paper proposes a fuzzy information-driven framework for quantum metric learning. This framework leverages fuzzy learning to accurately describe the uncertainty of data characteristics and adaptively integrates features, fuzziness, and uncertainty. Numerical experiments demonstrate that, compared to standard quantum metric learning, this framework achieves competitive performance and promising results. Furthermore, the interpretability provided by fuzzy logic aids in understanding the intrinsic mechanisms of the selected features during the quantum feature mapping process, offering new perspectives and approaches for better utilization of current quantum information processors.