  The topic area of this paper parameterized quantum circuits (quantum neural
networks) which are trained to estimate a given function, specifically the type
of circuits proposed by Mitarai et al. (Phys. Rev. A, 2018). The input is
encoded into amplitudes of states of qubits. The no-cloning principle of
quantum mechanics suggests that there is an advantage in redundantly encoding
the input value several times. We follow this suggestion and prove lower bounds
on the number of redundant copies for two types of input encoding. We draw
conclusions for the architecture design of QNNs.
