预条件量子线性系统算法
Preconditioned quantum linear system algorithm
摘要：
我们描述了一种量子算法，该量子算法推广了量子线性系统算法[Harrow等人，物理修订版信函103，150502（2009）]到任意问题规范。我们开发了一个状态准备例程，可以初始化通用状态，显示如何简单的辅助测量可以用来计算许多感兴趣的数量，并集成了量子兼容的预处理器，大大扩展了问题的数量，可以实现指数加速的经典线性系统求解器。为了证明该算法的适用性，我们展示了它是如何被用来计算电磁散射截面的任意目标指数速度比最好的经典算法。
英文摘要：
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.
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