  Portfolio optimization is an inseparable part of strategic asset allocation
at the Czech National Bank. Quantum computing is a new technology offering
algorithms for that problem. The capabilities and limitations of quantum
computers with regard to portfolio optimization should therefore be
investigated. In this paper, we focus on applications of quantum algorithms to
dynamic portfolio optimization based on the Markowitz model. In particular, we
compare algorithms for universal gate-based quantum computers (the QAOA, the
VQE and Grover adaptive search), single-purpose quantum annealers, the
classical exact branch and bound solver and classical heuristic algorithms
(simulated annealing and genetic optimization). To run the quantum algorithms
we use the IBM Quantum\textsuperscript{TM} gate-based quantum computer. We also
employ the quantum annealer offered by D-Wave. We demonstrate portfolio
optimization on finding the optimal currency composition of the CNB's FX
reserves. A secondary goal of the paper is to provide staff of central banks
and other financial market regulators with literature on quantum optimization
algorithms, because financial firms are active in finding possible applications
of quantum computing.
