Pre-training Tensor-Train Networks Facilitates Machine Learning with
  Variational Quantum Circuits
Jun Qi Chao-Han Huck Yang Pin-Yu Chen Min-Hsiu Hsieh
Variational quantum circuit (VQC) is a promising approach for implementing
quantum neural networks on noisy intermediate-scale quantum (NISQ) devices.
Recent studies have shown that a tensor-train network (TTN) for VQC, namely
TTN-VQC, can improve the representation and generalization powers of VQC.
However, the Barren Plateau problem leads to the gradients of the cost function
vanishing exponentially small as the number of qubits increases, making it
difficult to find the optimal parameters for the VQC. To address this issue, we
put forth a new learning approach called Pre+TTN-VQC that builds upon the
TTN-VQC architecture by incorporating a pre-trained TTN to alleviate the Barren
Plateau problem. The pre-trained TTN allows for efficient fine-tuning of target
data, which reduces the depth of the VQC required to achieve good empirical
performance and potentially alleviates the training obstacles posed by the
Barren Plateau landscape. Furthermore, we highlight the advantages of
Pre+TTN-VQC in terms of representation and generalization powers by exploiting
the error performance analysis. Moreover, we characterize the optimization
performance of Pre+TTN-VQC without the need for the Polyak-Lojasiewicz
condition, thereby enhancing the practicality of implementing quantum neural
networks on NISQ devices. We conduct experiments on a handwritten digit
classification dataset to corroborate our proposed methods and theorems.