A Quantum Variational Approach to Phase-Only Pattern Synthesis

Phase-only pattern synthesis is a long-standing and hard to solve problem in antenna engineering. Due to its non-linear nature, this kind of optimization problem is classically approached with iterative algorithms, where the convergence time depends on the problem topology. Often these heuristic solution routines get stuck in local optima and yield sub-optimal results. This paper addresses phase-only pattern synthesis by using a variational quantum algorithm, the quantum approximate optimization algorithm (QAOA). In this context, a mathematical approach is presented, which discretizes the optimization variables and allows representing the original non-linear functional as a higher-order polynomial. In contrast to other series expansion techniques it turns out that this polynomial has finite length without introducing any approximations. This makes phase-only patterns synthesis problems suitable to be solved on quantum computers with standard gate sets. The mathematical treatment of this optimization problem is complemented by a complexity analysis and a performance analysis. Finally, the challenges regarding future deployment of quantum approximate optimization for phase-only pattern synthesis are discussed.