论文标题
数据编码对变分量子机学习模型的表达能力的影响
The effect of data encoding on the expressive power of variational quantum machine learning models
论文作者
论文摘要
量子计算机可以通过将参数化的量子电路作为映射数据输入到预测的模型来用于监督学习。尽管已经做了许多工作来研究这种方法的实际含义，但这些模型的许多重要理论特性仍然未知。在这里，我们研究了将数据编码为模型的策略如何影响参数化量子电路的表达能力作为函数近似器。我们表明，一个人可以自然地将量子模型写为数据中的部分傅立叶系列，在该数据中，可访问的频率由电路中数据编码门的性质确定。通过重复多次编码门的简单数据，量子模型可以访问越来越丰富的频谱。我们表明，存在量子模型，可以实现所有可能的傅立叶系数集，因此，如果可访问的频谱在渐近较不富裕的情况下，则这些模型是通用函数近似器。
Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many important theoretical properties of these models remain unknown. Here we investigate how the strategy with which data is encoded into the model influences the expressive power of parametrised quantum circuits as function approximators. We show that one can naturally write a quantum model as a partial Fourier series in the data, where the accessible frequencies are determined by the nature of the data encoding gates in the circuit. By repeating simple data encoding gates multiple times, quantum models can access increasingly rich frequency spectra. We show that there exist quantum models which can realise all possible sets of Fourier coefficients, and therefore, if the accessible frequency spectrum is asymptotically rich enough, such models are universal function approximators.
