AI 中文总结
研究光子量子电路可训练性，引入基于样本方差与电路方差之比的框架，应用于光子数可观测量，识别可训练与不可训练区域，发现不同多项式所需样本数量规律，还找到量子估计能加速的可观测量类别，确立光子变分量子计算为有前途平台。
AI 中文摘要
变分量子算法是近期量子计算的主要方法，但其可扩展性可能受贫瘠高原和解决损失景观中小变化的采样成本限制。本文研究无源线性光学量子电路的可训练性，引入基于样本方差与电路方差之比的框架。该框架确定解决局部损失差异和梯度到比例精度所需的电路样本数量。将此框架应用于光子数可观测量，识别出可训练和不可训练区域。通过分析结果和电路方差的数值观察多项式衰减支持，发现固定阶光子数多项式随着系统大小增加仅需要多项式数量的样本，而高阶多项式和基于输出概率的可观测量通常需要指数数量的样本。在可训练区域内，进一步识别出量子估计比多种经典方法实现多项式加速的可观测量类别。在这个家族中，神经网络可观测量提供一种实际构造，允许将测量结果有效地处理成所需多项式。这些结果将光子变分量子计算确立为近期应用的有前途平台。
英文摘要
Variational quantum algorithms are a leading approach to near-term quantum computing, but their scalability can be limited by barren plateaus and the sampling cost of resolving small changes in the loss landscape. Here, we study the trainability of passive linear-optical quantum circuits and introduce a framework based on the ratio of sample variance to circuit variance. This ratio determines the number of circuit samples required to resolve local loss differences and gradients to proportional accuracy. We apply this framework to photon-number observables and identify both trainable and non-trainable regimes. Supported by analytic results and a numerically observed polynomial decay of the circuit variance, we find that fixed-order photon-number polynomials require only polynomially many samples as the system size grows, whereas high-order polynomials and observables based on output probabilities generally require exponentially many samples. Within the trainable regime, we further identify classes of observables in which quantum estimation achieves a polynomial speed-up over multiple classical methods. Within this family, neural network observables provide one practical construction that allow measurement outcomes to be efficiently processed into the desired polynomial. These results establish photonic variational quantum computing as a promising platform for near-term applications.
Comments53 pages, 10 figures
