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In the era of noisy intermediate scale quantum devices, variational quantumcircuits (VQCs) are currently one of the main strategies for building quantummachine learning models. These models are made up of a quantum part and aclassical part. The quantum part is given by a parametrization $U$, which, ingeneral, is obtained from the product of different quantum gates. By its turn,the classical part corresponds to an optimizer that updates the parameters of$U$ in order to minimize a cost function $C$. However, despite the manyapplications of VQCs, there are still questions to be answered, such as forexample: What is the best sequence of gates to be used? How to optimize theirparameters? Which cost function to use? How the architecture of the quantumchips influences the final results? In this article, we focus on answering thelast question. We will show that, in general, the cost function will tend to atypical average value the closer the parameterization used is from a$2$-design. Therefore, the closer this parameterization is to a $2$-design, theless the result of the quantum neural network model will depend on itsparametrization. As a consequence, we can use the own architecture of thequantum chips to defined the VQC parametrization, avoiding the use ofadditional swap gates and thus diminishing the VQC depth and the associatederrors.

Restricting to the chip architecture maintains the quantum neural network accuracy, if the parameterization is a $2$-design