AI 中文总结
该研究指出量子机器学习的输入问题是永久瓶颈，三种标准编码的态制备成本为Θ(N)，消除了量子算法的部分优势，需高效态制备等才能获得优势。
AI 中文摘要
量子算法通常被默认提供输入态，且输入态的获取是免费的。当输入为经典数据时，这一惯例掩盖了一个成本，该成本常常超过其后续算法本身的成本。我们回顾了三种标准编码（基编码、幅度编码和Grover–Rudolph分布加载）在编译为硬件门集后实际产生的成本，并指出所得的Θ(N)界是一个计数定理，而非可通过改进硬件消除的工程限制。我们报告了一个代表性加载任务的实测门数：在n=8量子比特时，最优库实现需要247个CNOT门，且每增加一个量子比特，门数就会翻倍；而生成旋转角的经典预处理需要读取整个输入向量。我们展示了该成本如何消除量子幅度估计在蒙特卡洛积分中的二次优势，并指出同样的成本核算更广泛地限制了量子机器学习：使量子算法在经典数据上运行快速的强输入模型也支持经典反量化，而量子核方法对于Gram矩阵具有Θ(M²)的态制备成本，且无法摊销。我们解释说，要从量子机器学习中获得优势，需要高效可制备的态、设备生成的分布、变分学习的加载以及摊销制备，并以一份评估输入依赖优势主张的清单作结。此处讨论的所有构造和测量的可执行笔记本均可获取。
英文摘要
Quantum algorithms are conventionally presented with their input state supplied for free. When the input is classical data, this convention conceals a cost that is frequently larger than the algorithm it precedes. We review what the three standard encodings, such as basis encoding, amplitude encoding, and Grover--Rudolph distribution loading, actually cost once transpiled to a hardware gate set, and argue that the resulting $Θ(N)$ bound is a counting theorem rather than an engineering limitation that improved hardware will remove. Measured gate counts for a representative loading task are reported: an optimal library implementation requires $247$ CNOT gates at $n=8$ qubits and doubles with each additional qubit, while the classical preprocessing that produces the rotation angles requires reading the entire input vector. We show how this cost eliminates the quadratic advantage of quantum amplitude estimation for Monte Carlo integration, and argue that the same accounting constrains quantum machine learning more broadly: the strong input models that make quantum algorithms fast on classical data also enable classical dequantization, and quantum kernel methods carry a $Θ(M^2)$ state-preparation cost for the Gram matrix that does not amortize. We explain that the efficiently preparable states, device-generated distributions, variationally learned loading, and amortized preparation are required to get advantage from quantum machine learning and close with a checklist for evaluating input-dependent advantage claims. Executable notebooks reproducing every construction and measurement discussed here are available.
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