10.5 Discrete Portfolio Optimisation with VQE
In Chapter 3, we investigated quantum annealing for NP-hard discrete portfolio optimisation problems. The same type of QUBO problems can be solved on gate model quantum computers with the help of a hybrid VQE algorithm. The QUBO formulation of the discrete portfolio optimisation problem consists of minimising the cost function (3.3.1):
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where q := (q1,…,qN) is a vector of binary decision variables indicating which (equally weighted) assets are selected (from the universe of N investable assets): qi = 1 means that asset i is selected and qi = 0 means that asset i is not selected. The task is to find a configuration of q that minimises L(q).
For each i,j = 1,…N, the coefficients ai, aj, and bij reflect, respectively, the individual and joint attractiveness of assets i and j. For example, assets with larger expected returns and lower volatilities would be assigned large negative...
