Quantum-inspired classification via efficient simulation of Helstrom measurement
Abstract: The Helstrom measurement (HM) is known to be the optimal strategy for distinguishing non-orthogonal quantum states with minimum error. Previously, a binary classifier based on classical simulation of the HM has been proposed. It was observed that using multiple copies of the sample data reduced the classification error. Nevertheless, the exponential growth in simulation runtime hindered a comprehensive investigation of the relationship between the number of copies and classification performance. We present an efficient simulation method for an arbitrary number of copies by utilizing the relationship between HM and state fidelity. Our method reveals that the classification performance does not improve monotonically with the number of data copies. Instead, it needs to be treated as a hyperparameter subject to optimization, achievable only through the method proposed in this work. We present a Quantum-Inspired Machine Learning binary classifier with excellent performance, providing such empirical evidence by benchmarking on eight datasets and comparing it with 13 hyperparameter optimized standard classifiers.
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