论文标题
在具有对数复杂性的量子寄存器中准备任意连续功能
Preparing Arbitrary Continuous Functions in Quantum Registers With Logarithmic Complexity
论文作者
论文摘要
量子计算机将能够通过其经典对应物的重要多项式和指数加速来解决重要问题，例如，金融方案和实际空间分子化学模拟中的选择定价。但是，只有在有效准备其输入的情况下，关键应用才能实现其潜在的加速。我们有效地解决了在所需分辨率和严格的误差范围内具有复杂性对数的任意连续（以及更通用）功能后有效制备量子状态的重要问题。这是通过基于Rank-1投影仪的仿真来开发基本子例程的。结合来自量子信息处理的各种技术，该子例程使我们能够提供一套用于解决实际任务的工具，例如状态准备，Lipschitz连续功能的数值整合以及概率密度函数的卓越采样。结果，我们的工作在广泛的应用中，例如财务预测和量子模拟都具有重要意义。
Quantum computers will be able solve important problems with significant polynomial and exponential speedups over their classical counterparts, for instance in option pricing in finance, and in real-space molecular chemistry simulations. However, key applications can only achieve their potential speedup if their inputs are prepared efficiently. We effectively solve the important problem of efficiently preparing quantum states following arbitrary continuous (as well as more general) functions with complexity logarithmic in the desired resolution, and with rigorous error bounds. This is enabled by the development of a fundamental subroutine based off of the simulation of rank-1 projectors. Combined with diverse techniques from quantum information processing, this subroutine enables us to present a broad set of tools for solving practical tasks, such as state preparation, numerical integration of Lipschitz continuous functions, and superior sampling from probability density functions. As a result, our work has significant implications in a wide range of applications, for instance in financial forecasting, and in quantum simulation.
