Optimization of the Quantum Backpropagation Algorithm for Improving the Quantum Support Vector Machine

The high-dimensional linear separability of the classic support vector machine is achieved through the kernel method, which maps data to a high-dimensional space. However, the kernel method involves estimating multiple parameters, which reduces the model's computational efficiency. To address this, some related works use quantum kernel estimation to replace the classic kernel method, thus reducing the computational load associated with parameter estimation in quantum support vector machines. Despite these improvements, quantum support vector machines face the challenge of establishing correlations between different data points through quantum entanglement to effectively capture the distribution characteristics of the data. Consequently, the model's accuracy is low when performing regression analysis on large datasets with complex distributions. To address this issue, an improved quantum backpropagation algorithm is introduced, utilizing controlled-Z gates to entangle qubits representing different data points. Additionally, to enhance the entanglement between qubits, the absolutely maximally entangled state is employed to further optimize the quantum backpropagation algorithm. This enhancement enables the algorithm to better capture the distribution characteristics of the data. Building on this, the quantum support vector machine model is improved to overcome the shortcomings of the existing model. A new algorithm is proposed, and the parameter count of the new algorithm's circuit is analyzed. Experimental results demonstrate that optimizing the quantum backpropagation algorithm to improve the quantum support vector machine leads to higher accuracy in regression analysis on real-world problems. Specifically, strengthening the degree of quantum entanglement makes the model more capable of capturing the distribution characteristics of complex datasets, resulting in more accurate fitting outcomes.