Quantum machine learning has become an area of growing interest but has certain theoretical and hardware-specific limitations. Notably, the problem of vanishing gradients, or barren plateaus, renders the training impossible for circuits with high qubit counts, imposing a limit on the number of qubits that data scientists can use for solving problems. Independently, angle-embedded supervised quantum neural networks were shown to produce truncated Fourier series with a degree directly dependent on two factors: the depth of the encoding and the number of parallel qubits the encoding applied to. The degree of the Fourier series limits the model expressivity. This work introduces two new architectures whose Fourier degrees grow exponentially: the sequential and parallel exponential quantum machine learning architectures. This is done by efficiently using the available Hilbert space when encoding, increasing the expressivity of the quantum encoding. Therefore, the exponential growth allows staying at the low-qubit limit to create highly expressive circuits avoiding barren plateaus. Practically, parallel exponential architecture was shown to outperform the existing linear architectures by reducing their final mean square error value by up to 44.7% in a one-dimensional test problem. Furthermore, the feasibility of this technique was also shown on a trapped ion quantum processing unit.

翻译：量子机器学习已成为一个日益受到关注的领域，但存在某些理论和硬件相关的限制。特别是，梯度消失问题（即贫瘠高原）使得高量子比特数的电路无法训练，限制了数据科学家可用于解决问题的量子比特数量。独立地，角度嵌入监督量子神经网络已被证明能产生截断傅里叶级数，其次数直接取决于两个因素：编码的深度和编码所应用的并行量子比特数量。傅里叶级数的次数限制了模型的表达能力。本文引入了两种新架构，其傅里叶次数呈指数级增长：序列指数量子机器学习架构和平行指数量子机器学习架构。这是通过高效利用编码时可用的希尔伯特空间实现的，从而提升了量子编码的表达能力。因此，指数级增长使得在低量子比特限制下创建高表达能力电路成为可能，从而避免贫瘠高原。实践中，平行指数架构被证明优于现有线性架构，在一维测试问题中其最终均方误差值降低了高达44.7%。此外，该技术的可行性也在一个离子阱量子处理单元上得到了验证。