Adaptive Non-Linear Quantum Neural Network for Multi- Class Image Classification

Abstract

Most of the used parameterized quantum circuit classifiers are created for binary problems and can later be generalized to multi-class problems via one-vs-all decomposition, which leads to a bigger number of models and higher costs of inference. In this paper, authors present Adaptive Non-Linear Quantum Neural Network (ANQNN) that performs direct classification of images into ten classes according to their eight-qubit statevector. Each 16×16 image is transformed into a vector of 256 features and divided into 32 sequential chunks of 8 features each that are processed sequentially. Prior to an encoding procedure, a special adaptive nonlinear transformation is applied to improve a simple linear term with trainable cubic and sinusoidal terms. Each chunk is encoded using the RY rotations and processed by means of subsequent chunk-specific RZ−RY−RZ rotations followed by controlled ring entanglement. During training, the adaptive angle of mixing influences the state of quantum mixture and at the end, 8 Pauli-Z expectation values are mapped to ten class logits via linear readout. The tests on MNIST and Fashion-MNIST datasets yielded 90.85% and 80.12% of accuracies respectively with mean one-vs-rest AUC values equaling to 0.9931 and 0.9748 respectively.The results indicate the viability of direct multi-class classification using sequential nonlinear feature encoding and parameterized quantum processing in the studied statevector setting, without asserting the existence of any general quantum computational advantage.