Researchers from the lab of the Institute on the Foundations of Computer Science at Universite Paris Diderot develop the first quantum algorithm for the constrained portfolio optimization problem. The algorithm has running time where variables are the number of: positivity and budget constraints, assets in the portfolio, desired precision, and problem-dependent parameters related to the well-conditioning of the intermediate solutions.
If only a moderately accurate solution is required, the quantum algorithm can achieve a polynomial speedup over the best classical algorithms in certain conditions. Researchers 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 a speedup over its classical counterpart
Mathematical finance is an application area where quantum computers could potentially offer groundbreaking speedups. This is a very recent research area for quantum algorithms and is important in terms of applications as even modest speedups for computational financial problems can have enormous real world impact. It has been suggested that quantum techniques like Feynman integrals could be useful for option pricing. There has also been experimental work where IBM quantum computers have been used to explore quadratic speedups for option pricing and using Monte Carlo methods.