Quantum Image Representations based Quantum Neural Networks for Binary Classification

We propose a comparative analysis of quantum image classification utilising a circularly-entangled quantum neural network (QNN) in conjunction with four quantum image representation (QIR) strategies: Novel Amplitude Square Sum (NASS), Quantum Block Image Representation (QBIR), Fourier-based Threshold Quantum Representation (FTQR), and Flexible Representation for Quantum Color Image (FRQCI). A methodical assessment of accuracy, loss convergence, and quantum resource requirements was made possible by the encoding of binary MNIST digits (0 and 1) at image sizes of \((2\times2)\), \((4\times4)\), and \((8\times8)\). Our findings demonstrate that, whereas QBIR-QNN offers competitive results with shallow circuits at the expense of greater qubit counts, NASS-QNN continuously converges to high training accuracy with stable parameters, achieving the most reliable and accurate performance. On the other hand, the instability and large resource overheads of FTQR-QNN and FRQCI-QNN restrict their applicability in the NISQ regime. The most promising approaches are highlighted by these results: NASS and QBIR, which provide workable trade-offs between hardware implementability, accuracy, and convergence stability.