The imminent of quantum computing devices opens up new possibilities for exploiting quantum machine learning (QML) [1, 2, 3] to improve the efficiency of classical machine learning algorithms in many new scientific domains like drug discovery [4] and efficient solar conversion [5]. Although the exploitation of quantum computing devices to carry out QML is still in its early exploratory states, the rapid development in quantum hardware has motivated advances in quantum neural network (QNN) to run in noisy intermediate-scale quantum (NISQ) devices [6, 7, 8, 9, 10], where not enough qubits could be spared for quantum error correction and the imperfect qubits have to be directly employed at the physical layer [11, 12, 13]. Even though, a compromised QNN is proposed by employing a quantum-classical hybrid model that relies on an optimization of the variational quantum circuit (VQC) [14, 15]. The resilience of the VQC to certain types of quantum noise errors and the high flexibility concerning coherence time and gate requirements admit VQC to apply to many promising applications on NISQ devices [16, 17, 18, 19, 20, 21, 22, 23]. Although many empirical studies of VQC for quantum machine learning have been reported, its theoretical understanding requires further investigation in terms of representation and generalization powers, particularly when the non-linear operator is employed for dimensionality reduction.