Higher-Order QAOA Outperforms Quadratic Version on IBM Quantum Hardware
A recent study led by Hamed Anwar has compared quadratic and higher-order formulations of the Quantum Approximate Optimisation Algorithm (QAOA) for solving optimisation problems. The team found that higher-order representations can deliver improved performance on current gate-based quantum computers.
The team developed a factoring method that significantly reduces the number of quantum gates needed to implement the higher-order version of QAOA. This method was applied to the HUBO version, resulting in a substantial reduction in the number of two-qubit gates on actual quantum hardware.
The study directly compared a standard Quadratic Unconstrained Binary Optimisation (QUBO) formulation with a Higher-Order Unconstrained Binary Optimisation (HUBO) approach using the same underlying problem instance. Experiments on IBM quantum hardware demonstrated that the higher-order formulation yields improved solution quality and better scaling in terms of qubit requirements, despite initially demanding more two-qubit gates.
The team systematically evaluated the performance of each algorithm based on solution quality, computational complexity, and consistency. The findings revealed that the higher-order approach delivers improved solution quality and better scalability compared to the quadratic approach for the same routing problem.
The study suggests that higher-order representations offer a promising pathway for tackling optimisation problems with improved performance on near-term quantum devices. Future work will focus on refining the factoring method and exploring its application to a wider range of problem instances to fully realise the benefits of higher-order representations within the QAOA framework.
