  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.
