Quantum Frank-Wolfe algorithms reduce dimension dependence in sparse convex optimization, from O(d) to O(sqrt d) function queries for vectors and from O(d^2) to O(d) per update step for matrices under certain assumptions.
A Quantum Online Portfolio Optimization Algorithm
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abstract
Portfolio optimization plays a central role in finance to obtain optimal portfolio allocations that aim to achieve certain investment goals. Over the years, many works have investigated different variants of portfolio optimization. Portfolio optimization also provides a rich area to study the application of quantum computers to obtain advantages over classical computers. In this work, 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.
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Quantum Algorithms for Projection-Free Sparse Convex Optimization
Quantum Frank-Wolfe algorithms reduce dimension dependence in sparse convex optimization, from O(d) to O(sqrt d) function queries for vectors and from O(d^2) to O(d) per update step for matrices under certain assumptions.