How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization

TL;DR

This paper introduces a toolkit for transforming a wide range of problems into QUBO form, enabling their solution via quantum optimization methods like QAOA and QA, demonstrated on ratio cut and logistic regression.

Contribution

It provides a systematic approach to approximate arbitrary problems as polynomials and convert them into QUBO, expanding the applicability of quantum optimization techniques.

Findings

Effective polynomial approximation of problems

Successful translation of polynomials to QUBO

Demonstrated on ratio cut and logistic regression

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).