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. The no-cloning principle of 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.

将近期量子计算机用于机器学习的一种建议是参数化量子电路（PQC）。在那里，输入以量子状态进行编码，应用依赖于参数的unit演化，最终测量出一个可观测值。以混合变量的方式，对参数进行训练，以使将输入分配给期望值的函数与目标函数匹配。的不克隆原则量子力学的作者建议对输入进行多次冗余编码是有好处的。在本文中，我们证明了PQC的期望值函数与给定目标函数匹配所必需的冗余副本数量的下限。我们为PQC的体系结构设计得出结论。