Quantum Two-Sample Test for Investment Strategies

29 Pages Posted: 16 Apr 2024 Last revised: 15 Nov 2024

See all articles by David Garvin

David Garvin

Rigetti Computing

Oleksiy Kondratyev

Imperial College London - Department of Mathematics

Alexander Lipton

Abu Dhabi Investment Authority

Marco Paini

Rigetti Computing

Date Written: April 9, 2024

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

Suggested Citation

Garvin, David and Kondratyev, Oleksiy and Lipton, Alexander and Paini, Marco, Quantum Two-Sample Test for Investment Strategies (April 9, 2024). Available at SSRN: https://ssrn.com/abstract=4789400 or http://dx.doi.org/10.2139/ssrn.4789400

David Garvin

Rigetti Computing

Oleksiy Kondratyev (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Alexander Lipton

Abu Dhabi Investment Authority

Marco Paini

Rigetti Computing ( email )

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