Particularly, we choose circuit 1, 2, 9, 14 and 15 in sim2019expressibility besides the QAOA-heuristic circuit. Then we evaluate the efficiency between completely different settings. 3 for each ”quantum” filter. Generally, the efficiency would enhance if we increase the number of layers of ansatz at the price of working time. Completely, we study 30 models for a similar coaching data with 2560 samples for 9 epochs. We first report outcomes on classification to show that our method works with fully-linked layers or not. Here, we examine the mannequin sensitivity to different variety of layers.
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The resulting construction is known as the quantum feature extraction layer. The key idea of our hybrid neural network is to implement the feature map within the convolutional layer with quantum parameterized circuits, and correspondingly, the output of this characteristic map is a correlational measurement on the output quantum state of the parameterized circuits. Totally different from Ref. henderson2020quanvolutional , which uses parameters mounted circuits, we can iteratively replace the parameters of circuits to get better efficiency.
Besides, we compare the performances of fashions with completely different ansaetze in several depths, showing that the mannequin with ansatz in excessive expressibility performs higher. We expect the introduction of QFE layers in additional architectures. This open question is left for future analysis. Extensive hyperparameter searches can enhance the efficiency. Besides, it’s famous that quantum neural tangent kernel (QNTK) theorynakaji2021quantum ; shirai2021quantum ; liu2021representation is developed just lately, which might be applied to QNNs. Nevertheless, there’s a no effective methodology to keep away from the barren plateaus yet. Alternatively, since the modern classical community are so deep and our methodology offers many prospects by way of PQCs, we cannot perform exhaustive assessments to search out the very best sequence of QFE layers and the best mixture of circuit ansaetze. In follow, the community architecture and the initialization technique have a big impression on efficiency. It will be attention-grabbing to investigate the model with QFE layers primarily based on the QNTK idea. Because of the big variety of selections of PQCs, we cannot carry out a brute force search for all the potentialities, while this opens a brand new house for the construction of hybrid quantum-classical networks.
Nonetheless, the filter in classical CNN mannequin is a generalized linear model (GLM). Recent works schuld2021effect ; goto2021universal ; liu2021hybrid proven that there exist PQCs that are universal operate approximators with a proper information encoding strategy. As a “micro network”, multilayer perceptron can improve the abstraction ability of the model. Combining these ideas, we change the linear filter with a PQC. In Network-in-Community (NiN) lin2013network , the linear filter replaced with a multilayer perceptron which is a basic operate approximator. In the sphere of QML, PQCs are thought-about as the “quantum network” buildings. It’s tough for linear filters to extract the concepts are typically highly nonlinear perform of the information patch.