Quantitative trading is an integral part of financial markets with high calculation speed requirements, while no quantum algorithms have been introduced into this field yet. We propose quantum algorithms for high-frequency statistical arbitrage trading in this work by utilizing variable time condition number estimation and quantum linear regression.The algorithm complexity has been reduced from the classical benchmark O(N^2d) to O(sqrt(d)(kappa)^2(log(1/epsilon))^2 )). It shows quantum advantage, where N is the length of trading data, and d is the number of stocks, kappa is the condition number and epsilon is the desired precision. Moreover, two tool algorithms for condition number estimation and cointegration test are developed.

翻译：量化贸易是计算速度要求高的金融市场的一个组成部分,而这一领域尚未引入量子算法。我们建议利用可变时间条件估计和量子线回归,为这项工作的高频统计套利交易提供量子算法。算法的复杂性已从传统的O(N ⁇ 2d)到O(sqrt(d)(kappa)§2(log(1/epsilon)))2。它显示了量子优势,N是交易数据长度,d是库存数量,Kappa是条件数字,Epsilon是预期精确度。此外,还开发了两种用于条件估计和合并测试的工具算法。