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The optimization of the power consumption of antenna networks is a problemwith a potential impact in the field of telecommunications. In this work, weinvestigate the application of quantum algorithms to the solution of asimplified model in this field using a statevector emulator. Specifically, weapply the quantum approximate optimization algorithm (QAOA) and the quantumadiabatic algorithm (QAA) to the antenna placement problem. We compare thesetwo algorithms in terms of solution quality by means of selected evaluationmetrics such as the approximation ratio, the probability of the exact solution,and the cumulative probability of cost-effective solutions.We corroborateprevious observations that QAA exhibits better performances when arbitrarilydeep circuits are allowed, while QAOA performs better at low depths. Bothapproaches in principle correctly identify the solution to the problem at asufficiently large depth. However, they suffer from an exponential decrease ofthe probability of the exact state, as the system size increases. This issue isparticularly severe when we include soft constraints in the problem, resultingin an effective full connectivity between the antennas. Our results suggestthat the low probability of measuring an acceptable solution is a potentialbottleneck in the application of these two algorithms to industrial problems atscales relevant to practical applications.

Beyond Theory: Evaluating the Practicality of Quantum Optimization Algorithms for Prototypical Industrial Applications