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« Paper » of the week: Quantum Algorithms for Portfolio Optimization by Iordanis Kerenidis, Anupam Prakash, and Dániel Szilágyi



Every week, Quantaneo selects from the scientific literature an academic article about quantum computing. We do not claim to judge the content of published articles. It is a purely subjective choice, of an article that interested the editorial team and that we would like to share with you.


September 4th 2019 | 299 readers

Photo by Claudia on Unsplash
Photo by Claudia on Unsplash
This week: Quantum Algorithms for Portfolio Optimization by Iordanis Kerenidis, Anupam Prakash, and Dániel Szilágyi
 
Date of publication: 22/08/2019
To cite this paper: arXiv:1908.08040 [math.OC]

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« Paper » of the week: Quantum Algorithms for Portfolio Optimization by Iordanis Kerenidis, Anupam Prakash, and Dániel Szilágyi
Abstract : We develop the first quantum algorithm for the constrained portfolio optimization problem. The algorithm has running time (see image above), where r is the number of positivity and budget constraints, n is the number of assets in the portfolio, ϵ the desired precision, and δ,κ,ζ are problem-dependent parameters related to the well-conditioning of the intermediate solutions. If only a moderately accurate solution is required, our quantum algorithm can achieve a polynomial speedup over the best classical algorithms with complexity (see image above), where ω is the matrix multiplication exponent that has a theoretical value of around 2.373, but is closer to 3 in practice. We also provide some experiments to bound the problem-dependent factors arising in the running time of the quantum algorithm, and these experiments suggest that for most instances the quantum algorithm can potentially achieve an O(n) speedup over its classical counterpart.

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