the best possible choice according to some criteria. The scenario we target is a Fund of Funds portfolio manager who is facing a task of selecting the best funds that follow particular trading strategies (e.g., EM Macro Funds) in order to maximize the risk-adjusted returns according to some model.

A realistic case occurs when the assets are selected with equal preference weights (a classical example of exposure to equally weighted assets is the CSO[^1] portfolio). Should we want to generalize the portfolio with larger allocation to a given asset, we could allow for multiples of the reference weight by cloning an asset and treating it as a new one.

The task of encoding the relationship among the choices of $M$ funds ([*without replacement*]{}) from the universe of $N$ funds can then be formulated as a quadratic form: $$\label{eq:QUBO}
O({\bf q}) = \sum_{i=1}^{N} a_i q_i + \sum_{i=1}^{N} \sum_{j=i+1}^{N} b_{ij} q_i q_j \; ,$$

where $q_i = 1$ means that asset $i$ is selected and $q_i = 0$ means that asset $i$ is not selected. Coefficients $a_i$ reflect asset attractiveness on a standalone basis and can be derived from the individual asset’s expected risk-adjusted returns. Coefficients $b_{ij}$ reflect pairwise diversification penalties (positive 