Generating quantum feature maps for SVM classifier

Abstract: We present and compare two methods of generating quantum feature maps for quantum-enhanced support vector machine, a classifier based on kernel method, by which we can access high dimensional Hilbert space efficiently. The first method is a genetic algorithm with multi-objective fitness function using penalty method, which incorporates maximizing the accuracy of classification and minimizing the gate cost of quantum feature map circuit. The second method uses variational quantum circuit, focusing on how to contruct the ansatz based on unitary matrix decomposition. Numerical results and comparisons are presented to demonstrate how the fitness fuction reduces gate cost while remaining high accuracy and conducting circuit through unitary matrix obtains even better performance. In particular, we propose some thoughts on reducing and optimizing the gate cost of a circuit while remaining perfect accuracy.