Enhancing the performance of variational quantum models by optimizing observable measurement based on generalization bounds

In the noisy intermediate-scale quantum computer (NISQ) era, parameterized quantum circuits play a key role as the mainstream model in quantum machine learning. Although this model has great potential in machine learning, its generalization performance still needs to be explored in depth. In this paper, under the background of supervised learning, the generalization performance and circuit optimization of parametric quantum circuit models are studied. We prove theoretically the effect of the F-norm of the measurement operator on the generalization bound of the parametric quantum machine learning model based on margin loss function and emphasize on improving the model performance by controlling the model complexity. Based on this, we focus on constructing measurement operators through the combination of convex quadratic programming and variational optimization to further improve the performance of the quantum machine learning model on unknown datasets. Finally, through the experimental simulation on PennyLane and the test on IBM real quantum computer, we verify the feasibility of the scheme. In conclusion, we provide a new idea for the design of quantum models through the study of generalization theory.