Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits

Abstract: Variational quantum circuits (VQCs) hold promise for quantum machine learning on noisy intermediate-scale quantum (NISQ) devices. While tensor-train networks (TTNs) can enhance VQC representation and generalization, the resulting hybrid model, TTN-VQC, faces optimization challenges due to the Polyak-Lojasiewicz (PL) condition. To mitigate this challenge, we introduce Pre+TTN-VQC, a pre-trained TTN model combined with a VQC. Our theoretical analysis, grounded in two-stage empirical risk minimization, provides an upper bound on the transfer learning risk. It demonstrates the approach's advantages in overcoming the optimization challenge while maintaining TTN-VQC's generalization capability. We validate our findings through experiments on quantum dot and handwritten digit classification using simulated and actual NISQ environments.