| Quantum neural network(QNN)that utilizes the structure of variational quantum algorithm(VQA)to build an artificial neural network,shows appealing performance in varieties of scenarios based on the power of quantum computers and quantum resources.However,in the era of NISQ,there is no quantum algorithm that is able to get rid of noise,which results in a decrease in accuracy and an increase in the cost of the training of QNNs,even the inability to train.Although researchers have been working on error mitigation methods for VQAs,fewer methods analyze from the aspect of gradient and encoding scheme of QNNs.Also,some noise mitigation protocols that are based on error correction code cost plenty of post-processing,which results in an increase in the cost of training due to the massive iteration of QNN,and the extra need for quantum resources.It is of theoretical and practical importance to research the methods to achieve noise reduction for QNN.In this dissertation,we analyze the impact of noise on QNNs and try to design noise reduction methods to enhance the robustness of the model and reduce the training cost.The main content of our research can be summarized in the following two points:1)We conduct an analysis of the effect of noise on QNN in the aspect of gradient and gain a linear mapping that describes the relation between gradients of QNN in noisy and noiseless environments.Then,an error mitigation method is proposed,which adds Gaussian noise and clips the gradient during the training of a QNN.The Gaussian noise is used to enhance the model’s robustness,and gradient clipping shuts down the noisy gradients that interfere with the direction of the trainable parameters’updating.We tested the performance of our method in several typical noise channels and noise models sampled from IBMQ quantum computers,the experiment results proved the effectiveness of our method in different noise models and classification tasks.Besides,our method does not cost extra quantum resources and is easy to combine with other error mitigation methods.2)For a specific structure of QNN,i.e.,data re-uploading model,we analyze its characteristic that the effect of noise tends to accumulate with the increasing of layers and further present an error mitigation method.The method puts Gaussian perturbations of different scales on the data samples according to the layers and injects a rotation gate as a neutralization of the last layer’s perturbation.Considering the property that perturbations at lower layers have a greater impact on the outputs of the model,we implement a strategy that the scale of Gaussian perturbation increases with the layers.We also demonstrate that the perturbations and the rotation gates injection do not change the original structure of the model.Finally,we verified the performance of our method on different classification tasks and noise models,and the experiment results showed our method’s effectiveness in enhancing the robustness of the data reuploading model.In addition,it is easy to implement our method in current quantum computers,which only costs O(n)quantum gates and classical operations that can be per-computed for an n-layer model. |
