Quantum Optimization Advances with Scalable 50-Qubit QAOA for NISQ Hardware

Quantum optimisation seeks to find the best solution from a vast number of possibilities, a challenge that currently strains even the most powerful computers, and researchers are now exploring ways to harness the principles of quantum mechanics to tackle these complex problems. Sebastián Saavedra-Pino, Ricardo Quispe-Mendizábal, and Gabriel Alvarado Barrios, alongside colleagues at institutions including the University of Ulster and the Universidad de Santiago de Chile, present a new approach called Fixed-Parameter-Count Approximate Quantum Optimisation, or FPC-QAOA. This innovative framework achieves scalability by maintaining a constant number of adjustable parameters, irrespective of the problem’s size or complexity, a significant departure from conventional methods that often require exponentially increasing resources. The team demonstrates that FPC-QAOA not only matches but frequently surpasses the performance of standard quantum algorithms, while dramatically reducing the computational burden, and importantly, experiments on real quantum hardware confirm its robustness and efficiency, paving the way for practical optimisation solutions on near-term quantum devices.

This innovative framework achieves scalability by maintaining a constant number of adjustable parameters, irrespective of the problem’s size or complexity, a significant departure from conventional methods that often require exponentially increasing resources.

The team demonstrates that FPC-QAOA not only matches but frequently surpasses the performance of standard quantum algorithms, while dramatically reducing the computational burden. Importantly, experiments on real quantum hardware confirm its robustness and efficiency, paving the way for practical optimisation solutions on near-term quantum devices.

The method separates schedule function optimisation from circuit digitisation, enabling accurate schedule approximations with minimal parameters while supporting arbitrarily deep digitised adiabatic evolutions, constrained only by current Noisy Intermediate-Scale Quantum (NISQ) hardware capabilities. Experiments demonstrate that FPC-QAOA achieves performance comparable to, or exceeding, standard QAOA while requiring nearly constant classical computational effort and significantly fewer evaluations of the quantum circuit itself. Tests were conducted on random MaxCut instances and the Tail Assignment Problem, showcasing the algorithm’s effectiveness across different optimization challenges.

The research team successfully implemented and tested FPC-QAOA on the IBM Kingston superconducting processor, utilizing up to 50 qubits, and confirmed its robustness and efficiency under realistic conditions with inherent noise. Measurements confirm that the method avoids the “barren plateau” effect, a common issue in deep quantum circuits where gradients vanish and optimization fails, by mitigating overparameterization.

The team’s work delivers a practical and scalable paradigm for variational quantum optimization, paving the way for tackling complex problems on near-term quantum devices, and establishing a foundation for future advancements in quantum computing applications. This innovative method separates the optimization of the circuit’s timing from the circuit’s structure, allowing for the creation of deeper, more complex circuits without a corresponding increase in the number of parameters that require classical optimization.

By maintaining a constant number of parameters, the team effectively mitigates challenges such as unstable training and overparameterization, problems that often hinder the performance of deeper quantum circuits. The team demonstrated that FPC-QAOA achieves performance comparable to, or exceeding, standard QAOA techniques on benchmark problems including random MaxCut instances and the Tail Assignment Problem, while requiring significantly fewer computational resources for optimization.

Experiments conducted on actual superconducting quantum hardware, specifically the IBM Kingston processor with up to 50 qubits, confirmed the robustness and efficiency of the method under realistic conditions with noise. While acknowledging that performance gains were less pronounced on certain network topologies, such as star graphs, the researchers consistently observed improvements or maintained competitive results across various problem structures and depths.

The authors note that the performance of FPC-QAOA is influenced by the underlying network topology of the problem being solved, and further investigation into optimizing the method for specific graph structures could yield additional benefits. Future work will likely focus on exploring the application of this fixed-parameter-count approach to a wider range of optimization problems and investigating its potential for integration with error mitigation techniques to further enhance performance on near-term quantum devices. These findings establish FPC-QAOA as a promising and scalable paradigm for tackling optimization challenges with available quantum technology.