论文标题
简化具有量子奇异值转换的经典量子算法插值
Simplifying a classical-quantum algorithm interpolation with quantum singular value transformations
论文作者
论文摘要
相位估计的问题（或振幅估计）接受了二次量子加速。 Wang，Higgott和Brierley [2019，物理学。莱特牧师。 122 140504]表明，量子加速和电路深度之间存在连续的权衡（通过定义一种称为$α$ -QPE的算法家族）。在这项工作中，我们表明$α$ -QPE的缩放可以自然而简洁地得出量子奇异价值转换（QSVT）的框架。从QSVT的角度来看，更多的连贯的Oracle调用转化为符号函数的更好多项式近似，这是解决相位估计的关键例程。符号函数的近似值越好，准确确定符号所需的样本越少。有了这个想法，我们简化了$α$ -QPE的证明，同时提供了对插值参数的新解释，并证明QSVT是关于经典量词插值推理的有希望的框架。
The problem of Phase Estimation (or Amplitude Estimation) admits a quadratic quantum speedup. Wang, Higgott and Brierley [2019, Phys. Rev. Lett. 122 140504] have shown that there is a continuous trade-off between quantum speedup and circuit depth (by defining a family of algorithms known as $α$-QPE). In this work, we show that the scaling of $α$-QPE can be naturally and succinctly derived within the framework of Quantum Singular Value Transformation (QSVT). From the QSVT perspective, a greater number of coherent oracle calls translates into a better polynomial approximation to the sign function, which is the key routine for solving Phase Estimation. The better the approximation to the sign function, the fewer samples one needs to determine the sign accurately. With this idea, we simplify the proof of $α$-QPE, while providing a new interpretation of the interpolation parameters, and show that QSVT is a promising framework for reasoning about classical-quantum interpolations.
