How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization

Abstract: Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a toolkit of methods to transform almost arbitrary problems to QUBO by (i) approximating them as a polynomial and then (ii) translating any polynomial to QUBO. We showcase the usage of our approaches on two example problems (ratio cut and logistic regression).