QUBO
QUBO stands for Quadratic Unconstrained Binary Optimization. It denotes a class of optimization problems in which the decision variables x_i take binary values in {0,1}, and the objective is a quadratic function: minimize f(x) = x^T Q x, where Q is a real symmetric matrix. Because x_i^2 = x_i for binary variables, the diagonal entries contribute linear terms and the off-diagonal entries encode pairwise interactions. The problem is unconstrained in the sense that x is restricted only to binary values; constraints are typically incorporated by adding penalty terms to the objective, yielding a pure QUBO objective over binary variables.
QUBO and the Ising model are equivalent representations of the same optimization task. By mapping binary variables
QUBO is used to formulate a wide range of NP-hard problems, such as maximum cut, maximum independent
Solving a QUBO involves finding a binary vector x that minimizes x^T Q x. The problem size