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Quantum Algorithms for High-Frequency Statistical Arbitrage

Article arXiv papers · Author: Xi-Ning Zhuang et al.
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Summary

The paper proposes a quantum approach to high-frequency statistical arbitrage across stocks. It combines variable-time condition-number estimation with quantum linear regression, and also develops supporting methods for estimating condition numbers and testing cointegration.

The authors compare the stated complexity with a classical benchmark, expressing the quantum method in terms of the number of stocks, the condition number, and target precision rather than trading-data length. This is a theoretical complexity claim, not evidence of live trading performance. The provided description gives no empirical evaluation, implementation details, or discussion of practical hardware constraints, so it does not establish whether the proposed speedup translates into usable trading systems.

Key ideas

  • The proposed arbitrage method uses quantum linear regression and variable-time condition-number estimation.
  • It includes separate tools for condition-number estimation and cointegration testing.
  • The stated complexity depends on the number of stocks, conditioning, and desired precision.
  • The described quantum advantage is a computational claim, with no live-market validation given.

Tags

EquitiesArbitrageHigh-frequency tradingStatistics
Full text
# Quantum Quantitative Trading: High-Frequency Statistical Arbitrage Algorithm


# Quantum Quantitative Trading: High-Frequency Statistical Arbitrage Algorithm









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.