New Paper: Symmetries unlock hidden patterns in quantum algorithms

An international team of scientists from Forschungszentrum Jülich (Germany) and Los Alamos National Laboratory (USA) has uncovered new insights into a promising quantum algorithm for solving complex optimization problems: the Quantum Approximate Optimization Algorithm (QAOA). Using symmetries, the researchers have revealed hidden patterns that govern how QAOA finds solutions. This algorithm is particularly well suited for quantum simulators, such as those studied in the EU projects HPCQS and PASQuanS2.1.

The Quantum Approximate Optimization Algorithm (QAOA) is designed to tackle challenging optimization problems on near-term quantum computers and simulators. It combines quantum operations with classical optimization steps to find near-optimal solutions efficiently.

The research team has developed a symmetry framework to analyze QAOA and its variants. This framework enables precise mathematical predictions of the algorithm’s behavior, going beyond what numerical simulations alone can achieve. These structural insights guide the design and selection of QAOA variants for optimal performance.

Importantly, the symmetry framework can be applied to a wide range of quantum algorithms. By revealing hidden patterns and structures, symmetries provide a powerful tool for understanding quantum algorithms more systematically — paving the way for a more efficient use of quantum resources. These results also advance our understanding of how quantum simulators can address practical optimization challenges.

The results were published in PRX Quantum, and the full paper is available online.