Quantum Two-Sample Test for Investment Strategies

Abstract

We demonstrate the benefits of using a quantum algorithm rather than its classical counterpart on one of the most fundamental problems of quantitative finance – classification of probability distributions. This problem has many direct applications to practical financial use cases including time series analysis, detection of structural breaks, and monitoring of alpha decay. We present an efficient quantum two-sample test analogous to the classical maximum mean discrepancy test. Experimental results are obtained on Rigetti's Ankaa-2 quantum computer, applied to a specific instance of the probability distribution classification problem. A comparison with the classical maximum mean discrepancy benchmark is provided. The quantum algorithm performs better in terms of discriminatory power. Additionally, the quantum algorithm scales linearly with the number of data samples versus a quadratic scaling for the classical benchmark.

Keywords: density matrix, financial time series, Frobenius distance, maximum mean discrepancy, parameterised quantum circuit, quantum computing, two-sample test

JEL Classification: C02, C14, C63, C88, G11