Input Redundancy for Parameterized Quantum Circuits

One proposal to utilize near-term quantum computers for machine learning are Parameterized Quantum Circuits (PQCs). There, input is encoded in a quantum state, parameter-dependent unitary evolution is applied, and ultimately an observable is measured. In a hybrid-variational fashion, the parameters are trained so that the function assigning inputs to expectation values matches a target function. Theno-cloning principleof quantum mechanics suggests that there is an advantage in redundantly encoding the input several times. In this paper, we prove lower bounds on the number of redundant copies that are necessary for the expectation value function of a PQC to match a given target function. We draw conclusions for the architecture design of PQCs.