论文标题
通用的量子内部产品和金融工程的应用
A Generalized Quantum Inner Product and Applications to Financial Engineering
论文作者
论文摘要
在本文中，我们提出了一种规范量子计算方法，以估计离散函数f和真实权重w（k）所采用的值的加权总和w（k）f（k）。该方法的规范方面来自依赖于量子状态振幅中编码的单个线性函数，并使用符号纠缠来编码函数f。 我们通过将函数值映射到哈希来进一步扩展此框架，以估算具有真实哈希h的Hashed函数值的加权总和W（k）h（f（k））。这种概括允许计算受限制的加权总和，例如处于风险的价值，比较器以及Lebesgue积分和统计分布的部分力矩。 我们还引入了必不可少的构建块，例如标准化线性量子状态和正常分布的有效编码。
In this paper we present a canonical quantum computing method to estimate the weighted sum w(k)f(k) of the values taken by a discrete function f and real weights w(k). The canonical aspect of the method comes from relying on a single linear function encoded in the amplitudes of a quantum state, and using register entangling to encode the function f. We further expand this framework by mapping function values to hashes in order to estimate weighted sums w(k)h(f(k)) of hashed function values with real hashes h. This generalization allows the computation of restricted weighted sums such as value at risk, comparators, as well as Lebesgue integrals and partial moments of statistical distributions. We also introduce essential building blocks such as efficient encodings of standardized linear quantum states and normal distributions.
