generation D-Wave machines solving discrete portfolio optimization problems [@rosenberg2016solving; @marzec2016portfolio]. The discrete portfolio optimization problem is much harder to solve than continuous mean-variance portfolio optimization problem due to strong non-linearity, and is known to be NP-complete [@kellerer2000selecting].

In this paper we propose an original approach to portfolio optimization that extends the mean-variance model to a general dependence structure and allows portfolio managers to express discretionary views on relative attractiveness of different assets and their combinations. The manuscript is structured as follows: in Section \[sec:problem\] the formulation of the portfolio optimization problem is constructively described starting from real market data. Section \[sec:annealer\] describes the hybrid quantum annealing solver and its setup. Section \[sec:main\] is devoted to the experimental results, including results obtained with the classical Genetic Algorithm (GA) benchmark (following [@Kondratyev2017risk]). In Section \[sec:conclusion\] we conclude with a discussion and considerations for future work.\

Portfolio Optimization Beyond Markowitz {#sec:problem}
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The problem we are trying to solve here is construction of the optimal portfolio from the assets with known characteristics such as asset returns, volatilities and pairwise correlations. A typical portfolio optimization problem consists of selecting $M$ assets from the universe of $N$ investible assets. These $M$ assets should ideally be 