Constraint-preserving quantum algorithm for the multi-frequency antenna placement problem

TL;DR

This paper introduces a constraint-preserving quantum adiabatic algorithm for the multi-frequency antenna placement problem, demonstrating improved feasibility and success rates over basic quantum approaches and competitive performance with classical methods.

Contribution

The paper presents a novel quantum algorithm that preserves problem constraints, enhancing efficiency and scalability for a specific telecommunications optimization problem.

Findings

Quantum algorithm outperforms basic QAA in feasibility and success probability.

Demonstrates competitive results against classical methods like branch-and-bound and simulated annealing.

Extension potential to other constrained optimization problems.

Abstract

Quantum algorithms for combinatorial optimization typically encode constraints as soft penalties within the objective function, which can reduce efficiency and scalability compared to state-of-the-art classical methods that instead exploit constraints to guide the search toward high-quality solutions. Although solving this issue for an arbitrary problem is inherently a hard task, we address this challenge for a specific problem in the field of telecommunications, the multi-frequency antenna placement problem, by introducing a constraint-preserving quantum adiabatic algorithm (QAA). To this aim, we construct a quantum circuit that prepares an initial state comprising an equal superposition of all feasible solutions, and define a custom mixer that preserves both the one-hot encoding constraint for vertex coloring and the cardinality constraint on the number of antennas. This scheme can be extended to a broader range of applications characterized by similar constraints. We first benchmark the performance of this quantum algorithm against a basic version of QAA, demonstrating superior performance in terms of feasibility and success probability. We then apply this algorithm to large problem sizes with hundreds of variables using a constraint-aware decomposition method based on the SPLIT framework. Our results indicate competitive performance against other large-scale classical approaches, such as branch-and-bound and simulated annealing. This work supports previous claims that constraint-aware algorithms are crucial for the practical and efficient application of quantum methods in industrial settings.