Constraint-preserving Quantum Algorithm Solves Multi-Frequency Antenna Placement with Feasible Solution Superposition

The efficient placement of antennas is a critical challenge in modern telecommunications, often requiring complex optimisation problems with strict limitations on possible solutions. Matteo Vandelli, Francesco Ferrari, and Daniele Dragoni, from Quantum Computing Solutions and the Hypercomputing Continuum Unit at Leonardo S. p. A., now present a new quantum algorithm that directly incorporates these constraints, rather than treating them as obstacles to overcome. Their approach constructs a quantum circuit that begins with only valid antenna configurations and then evolves this state to find the best solution, significantly improving both the reliability and success rate compared to standard quantum algorithms. This constraint-preserving method demonstrates competitive performance against established classical techniques, even when applied to large, complex antenna placement scenarios with hundreds of variables, and supports the growing evidence that constraint-aware quantum algorithms are essential for practical industrial applications.

Variational Algorithms for Quantum Optimization

Research centers on quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing, exploring their performance and scalability compared to classical methods. Scientists are investigating how these algorithms can outperform traditional approaches, particularly for complex problems. Theoretical foundations, such as adiabatic quantum computation, entangled states, and the importance of quantum coherence, underpin this work. A key goal is demonstrating a quantum advantage, where quantum algorithms solve problems intractable for classical computers, and that this speedup increases with problem size.

Variational principles are central to many of these algorithms, allowing researchers to optimize parameters and minimize energy functions. Practical implementation involves utilizing quantum hardware platforms, often superconducting qubit systems, and accelerating classical simulations with GPUs. Software tools like Qiskit, IBM ILOG CPLEX, Numba, and MPI4py facilitate algorithm development and execution. Recent studies suggest that QAOA is demonstrating scaling advantages on certain problems, and efficient methods for preparing entangled states are being developed.

Constraint Preservation Boosts Antenna Placement Optimisation

Scientists have developed a novel quantum adiabatic algorithm to address the multi-frequency antenna placement problem, a critical optimization challenge in telecommunications and disaster response. This new approach directly incorporates problem constraints into the algorithm, significantly improving performance compared to standard quantum methods. The team constructed a quantum circuit that begins with an equal superposition of all feasible solutions and employs a custom mixer that maintains both vertex coloring and cardinality constraints, ensuring solutions adhere to problem limitations. Experiments demonstrate the effectiveness of this method on problems with hundreds of variables, utilizing a constraint-aware decomposition method.

Results indicate competitive performance against established classical approaches, including branch-and-bound and simulated annealing, highlighting the potential of constraint-aware quantum algorithms for large-scale optimization. The algorithm utilizes a one-hot encoding scheme to represent variables and defines a cost function that balances maximizing coverage with minimizing interference. Researchers formulated the problem as placing antennas on candidate locations, selecting from possible frequencies, and defined a cost function to quantify solution quality. This function incorporates area coverage, interference between antennas, and a penalty term to enforce constraints, ensuring realistic and effective antenna placement.

Constraint Preservation Improves Antenna Placement Algorithms

This research presents a novel approach to solving complex optimization problems, specifically the multi-frequency antenna placement problem, by directly incorporating constraints into the algorithm rather than treating them as penalties. Scientists developed a constraint-preserving adiabatic algorithm that begins by establishing an initial state encompassing all viable solutions and utilizes a custom mixer to maintain both vertex coloring and cardinality constraints. Benchmarking against a standard adiabatic algorithm demonstrates improved feasibility and success rates, while application of a constraint-aware decomposition method enables the algorithm to tackle problems with hundreds of variables. The results indicate that this hybrid quantum-classical approach achieves solution quality within 5% of the optimal result and matches the performance of established classical solvers. This research supports the idea that focusing on problem-centric solutions can yield practical benefits even before the development of universally applicable constraint-handling methods in quantum computing. Future work may focus on extending these constraint-preserving techniques to a broader range of optimization problems encountered in industrial settings.