![]() This observation is supported by the theory on PAC learnability, which proves that VC dimension is upper bounded due to the locality and unitarity of the hardware-efficient ansatz. Thorough numerical simulations show that the expressibility and generalization error scaling of the ansatz saturate when the circuit depth increases, implying the automatic regularization to avoid the overfitting issue in the quantum circuit learning scenario. In this article, we perform simulations and theoretical analysis of the quantum circuit learning problem with hardware-efficient ansatz. However, it is not clear how the regularization interplays with the expressibility under the limitation of current Noisy-Intermediate Scale Quantum devices. It is conjectured that the unitarity of quantum circuits provides possible regularization to avoid overfitting. Applying quantum processors to model a high-dimensional function approximator is a typical method in quantum machine learning with potential advantage.
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