AI 中文总结
该研究提出了一种直接稳定的电路编译算法，可精确构造厄米特矩阵矩阵多项式的块编码，适用于两类标准输入模型，经典算法时间复杂度近最优，数值实验验证了其高效性。
AI 中文摘要
我们提出了一种直接且稳定的电路编译算法，该算法明确且精确地构造了厄米特矩阵的矩阵多项式的块编码。在统一框架下，该算法可直接应用于两种标准输入模型：块编码和哈密顿量模拟。对于次数为$d$的目标多项式，我们的经典算法达到了近最优的时间复杂度$\u039f(d\ud835\udcab d)$。数值结果证实，在标准CPU上，对于最高$10^7$次的多项式，其渐近缩放可在约一分钟内实现。我们通过开发一种通用的函数值对角块编码实现了这一点，该编码将标准量子态制备技术与基于插值的QSP框架相连接。
英文摘要
A recent interpolation-based Quantum Signal Processing (QSP) framework by Alase bypasses the phase-finding procedures required in conventional QSP, allowing for a direct encoding of the target polynomial into a quantum circuit. However, this approach assumes access to a diagonal block encoding of function values without providing an explicit circuit construction. In this work, we address this gap by developing an explicit circuit construction method for diagonal block encodings. The resulting algorithm achieves a computational cost of $\mathcal{O}(d\log d)$ for explicitly constructing block encodings of matrix polynomials, improving upon the best-known theoretical bounds of previous methods. Numerical results confirm this scaling, demonstrating that circuit parameters for polynomial degrees up to $10^7$ can be computed in about a minute on a standard CPU.
