A quantum online portfolio optimization algorithm

Debbie Lim, Patrick Rebentrost

Abstract: Portfolio optimization plays a central role in finance to obtain optimal portfolio allocations that aim to achieve certain investment goals. Portfolio optimization also provides a rich area to study the application of quantum computers to obtain advantages over classical computers. In a multi-period setting, we give a sampling version of an existing classical online portfolio optimization algorithm by Helmbold et al., for which we in turn develop a quantum version. The quantum advantage is achieved by using techniques such as quantum state preparation, inner product estimation and multi-sampling. Our quantum algorithm provides a quadratic speedup in the time complexity, in terms of n, where n is the number of assets in the portfolio. The transaction cost of both of our classical and quantum algorithms is independent of n which is especially useful for practical applications with a large number of assets.