论文标题
指数数据编码用于量子监督学习
Exponential data encoding for quantum supervised learning
论文作者
论文摘要
多元函数映射的可靠量子监督学习取决于相应的量子电路和测量资源的表达性。我们介绍了指数数据编码的策略，这些策略在所有非输入的Pauli编码方案中都是硬件有效且最佳的，这足以使量子电路仅使用几乎指数的编码门，表达具有非常宽的傅立叶频谱的一般函数。我们表明，这种编码策略不仅减少了量子资源，而且在培训期间与已知有效的经典策略相比，在多项式深度训练循环中也采用了实践资源优势。当计算资源受到限制时，我们从数值上证明，即使具有单层训练模块的指数数据编码电路通常也可以表达出位于经典可表达的区域之外的功能，从而支持这种资源优势的实际好处。最后，我们说明了指数编码在学习乙醇分子和加利福尼亚州住房价格的潜在能量表面时的性能
Reliable quantum supervised learning of a multivariate function mapping depends on the expressivity of the corresponding quantum circuit and measurement resources. We introduce exponential-data-encoding strategies that are hardware-efficient and optimal amongst all non-entangling Pauli-encoded schemes, which is sufficient for a quantum circuit to express general functions having very broad Fourier frequency spectra using only exponentially few encoding gates. We show that such an encoding strategy not only reduces the quantum resources, but also exhibits practical resource advantage during training in contrast with known efficient classical strategies when polynomial-depth training circuits are also employed. When computation resources are constrained, we numerically demonstrate that even exponential-data-encoding circuits with single-layer training modules can generally express functions that lie outside the classically-expressible region, thereby supporting the practical benefits of such a resource advantage. Finally, we illustrate the performance of exponential encoding in learning the potential-energy surface of the ethanol molecule and California's housing prices
