# An Exclusive-Sum-of-Products Pipeline for QAOA

## TL;DR

This paper introduces an ESOP-based method for encoding constraints in QAOA, improving approximation ratios for combinatorial problems like maximum independent set compared to traditional penalization techniques.

## Contribution

It presents a novel ESOP encoding approach for constraints in QAOA, demonstrating improved performance on maximum independent set problems.

## Key findings

- ESOP constraint formulations outperform standard penalization in approximation ratios.
- Up to 30.3% improvement in approximation ratios with ESOP encoding.
- Higher approximation ratios achieved after one QAOA layer on 64% of tested graphs.

## Abstract

The quantum approximate optimization algorithm is commonly used to solve combinatorial optimization problems. While unconstrained problems map naturally into the algorithm, incorporating constraints typically requires penalizing constraint violations in the objective function. In this work, we propose an alternative approach that encodes constraints as Boolean expressions in exclusive-sum-of-products (ESOP) form before penalization. We test this method on the maximum independent set problem using graphs with 3 to 20 vertices and find that ESOP constraint formulations achieve higher approximation ratios than standard constraint penalization methods, with percent increases of up to 30.3%. Furthermore, ESOP constraint formulations result in higher approximation ratios than standard QAOA penalization approaches after one layer of the algorithm on approximately 64% of the tested graphs.