Solving the Product Breakdown Structure Problem with constrained QAOA

TL;DR

This paper introduces a constrained QAOA approach tailored for the Product Breakdown Structure problem, effectively reducing the search space and mitigating barren plateau issues, with promising scalability and performance benefits.

Contribution

The paper presents a novel constrained QAOA method that inherently respects problem constraints, improving efficiency over traditional QAOA and quantum annealing approaches.

Findings

Reduced search space due to constraint-aware QAOA

Improved scalability and performance in experiments

Potential suppression of barren plateau effects

Abstract

Constrained optimization problems, where not all possible variable assignments are feasible solutions, comprise numerous practically relevant optimization problems such as the Traveling Salesman Problem (TSP), or portfolio optimization. Established methods such as quantum annealing or vanilla QAOA usually transform the problem statement into a QUBO (Quadratic Unconstrained Binary Optimization) form, where the constraints are enforced by auxiliary terms in the QUBO objective. Consequently, such approaches fail to utilize the additional structure provided by the constraints. In this paper, we present a method for solving the industry relevant Product Breakdown Structure problem. Our solution is based on constrained QAOA, which by construction never explores the part of the Hilbert space that represents solutions forbidden by the problem constraints. The size of the search space is thereby reduced significantly. We experimentally show that this approach has not only a very favorable scaling behavior, but also appears to suppress the negative effects of Barren Plateaus.