Effects of fitness function in genetically auto-generated quantum feature maps

Abstract

We present and probe some improvements over the method using genetic algorithm proposed in [S. Altares-López, Automatic design of quantum feature maps, (2021)] to automatically generate 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. In addition, we define a multi-objective fitness function using penalty method, which incorporates maximizing the accuracy of classification and minimizing the gate cost of quantum feature map's circuit as the original method. Numerical results and comparisons with different kernel methods as well as the original proposed method are presented to demonstrate the efficiency of our fitness function. In particular, we reduce and optimize the gate cost of a circuit shown in [J.R. Glick, Covariant quantum kernels for data with group structure, (2022)] from 51 to 3 while remaining perfect accuracy.