Quantum Quantitative Trading: High-Frequency Statistical Arbitrage Algorithm

TL;DR

This paper introduces quantum algorithms for high-frequency statistical arbitrage trading, significantly reducing computational complexity and demonstrating potential quantum advantage in financial data analysis.

Contribution

The paper presents novel quantum algorithms for arbitrage trading, including quantum linear regression and condition number estimation, with complexity improvements over classical methods.

Findings

Quantum algorithms reduce complexity from O(N^2d) to O(sqrt(d)(kappa)^2(log(1/epsilon))^2).

Quantum advantage demonstrated in high-frequency trading scenarios.

Two new quantum tool algorithms for condition number estimation and cointegration testing.

Abstract

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.