Figure 4.

Example QUBO for a system of second-order polynomial equations. The QUBO can be organized into four quadrants as indicated by the solid black lines, corresponding to bilinear (2^nd quadrant), tri-linear (1^st and 3^rd quadrants) and quadra-linear (4^th quadrant) contributions. Within the quadrants, the elements are colored to reflect the effective one (red), two (green), three (blue), and four (yellow) qubit interactions after accounting for repeated indices. The entries in ${\mathcal{Q}}^{sparse}$ are distributed to entries in the QUBO corresponding to the order of interaction: Q⁽¹⁾ to red, Q⁽²⁾ to green, Q⁽³⁾ to blue, Q⁽⁴⁾ to yellow. The coefficients of the constraint equations contributes to entries in red text.