释放基于脉冲的量子神经网络的表达能力
Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks
AI总结：
本文从量子控制理论出发，证明基于脉冲的量子神经网络在系综可控条件下可逼近任意非线性函数，并通过数值模拟展示其比基于门电路的模型具有更强的表达能力，为NISQ设备上的QML模型设计奠定理论基础。
摘要：
基于含噪声中等规模量子（NISQ）设备的量子机器学习（QML）依赖于对有限量子资源的最优利用。虽然基于门电路的QML模型对软件工程师来说用户友好，但其表达能力受限于有限相干时间内允许的电路深度。相比之下，基于脉冲的模型能够在相同时间内构建“无限”深的量子神经网络，这可能为复杂学习任务释放更大的表达能力。本文从量子控制理论的角度研究了这一潜力。我们首先指出，基于脉冲的模型的非线性来自编码过程，该过程可视为基于门电路的模型中数据重上传的连续极限。随后，我们证明当底层物理系统是系综可控时，基于脉冲的模型可以逼近任意非线性函数。在此条件下，数值模拟表明，通过增加脉冲长度或量子比特数量可以增强表达能力。正如预期，我们通过数值示例表明，与基于门电路的模型相比，基于脉冲的模型可以释放更多的表达能力。这些发现为使用NISQ设备理解和设计具有表达能力的QML模型奠定了理论基础。
英文摘要：
Quantum machine learning (QML) based on Noisy Intermediate-Scale Quantum (NISQ) devices hinges on the optimal utilization of limited quantum resources. While gate-based QML models are user-friendly for software engineers, their expressivity is restricted by the permissible circuit depth within a finite coherence time. In contrast, pulse-based models enable the construction of "infinitely" deep quantum neural networks within the same time, which may unleash greater expressive power for complex learning tasks. In this paper, this potential is investigated from the perspective of quantum control theory. We first indicate that the nonlinearity of pulse-based models comes from the encoding process that can be viewed as the continuous limit of data-reuploading in gate-based models. Subsequently, we prove that the pulse-based model can approximate arbitrary nonlinear functions when the underlying physical system is ensemble controllable. Under this condition, numerical simulations demonstrate the enhanced expressivity by either increasing the pulse length or the number of qubits. As anticipated, we show through numerical examples that the pulse-based model can unleash more expressive power compared to the gate-based model. These findings lay a theoretical foundation for understanding and designing expressive QML models using NISQ devices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
