Input Redundancy for Parameterized Quantum Circuits

In this paper we deal with a special type of parameterized quantum circuits, the so-called quantum neural networks or QNN's, which are trained to estimate a given function, specifically the type of circuits proposed by Mitarai et al.\ (Phys.\ Rev.\ A, 2018; see below). 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.