基于洛朗多项式的QSP处理的多数无害方法
Mostly Harmless Methods for QSP-Processing with Laurent Polynomials
AI总结：
本文提出一种基于洛朗多项式的QSP处理方法，无需优化或求根即可确定SU(2)旋转矩阵，并在浮点精度下验证了其在哈密顿量模拟等场景中的有效性。
摘要：
量子信号处理（QSP）及其扩展作为开发量子算法的框架日益流行。然而，QSP实现仍在完成一个经典预处理步骤（“QSP处理”）时面临困难，该步骤确定定义QSP电路的$SU(2)$旋转矩阵集合。我们引入一种针对复多项式的QSP处理方法，无需优化或求根即可确定解，并通过具有浮点精度系数的多项式验证了我们方法的成功。我们展示了该技术在相关目标多项式和精度区间上的成功，包括QSP哈密顿量模拟中使用的Jacobi-Anger展开。对于符号函数和反函数近似的常见选择，我们刻画了所有已知QSP处理方法在不使用任意精度算术的情况下预期会遇到困难的区间。
英文摘要：
Quantum signal processing (QSP) and its extensions are increasingly popular frameworks for developing quantum algorithms. Yet QSP implementations still struggle to complete a classical pre-processing step ('QSP-processing') that determines the set of $SU(2)$ rotation matrices defining the QSP circuit. We introduce a method of QSP-processing for complex polynomials that identifies a solution without optimization or root-finding and verify the success of our methods with polynomials characterized by floating point precision coefficients. We demonstrate the success of our technique for relevant target polynomials and precision regimes, including the Jacobi-Anger expansion used in QSP Hamiltonian Simulation. For popular choices of sign and inverse function approximations, we characterize regimes where all known QSP-processing methods should be expected to struggle without arbitrary precision arithmetic.
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