  In this letter we propose a general principle for how to build up a quantum
neural network with high learning efficiency. Our stratagem is based on the
equivalence between extracting information from input state to readout qubit
and scrambling information from the readout qubit to input qubits. We
characterize the quantum information scrambling by operator size growth, and by
Haar random averaging over operator sizes, we propose an averaged operator size
to describe the information scrambling ability for a given quantum neural
network architectures, and argue this quantity is positively correlated with
the learning efficiency of this architecture. As examples, we compute the
averaged operator size for several different architectures, and we also
consider two typical learning tasks, which are a regression task of a quantum
problem and a classification task on classical images, respectively. In both
cases, we find that, for the architecture with a larger averaged operator size,
the loss function decreases faster or the prediction accuracy in the testing
dataset increases faster as the training epoch increases, which means higher
learning efficiency. Our results can be generalized to more complicated quantum
versions of machine learning algorithms.
