Quantum Approximate Optimization Algorithm Performance Explored on Simulators and System One Hardware with Hundreds of Executions

The quest for practical quantum computation faces a fundamental hurdle, as real-world quantum devices inevitably introduce noise that degrades performance, unlike the clean results obtained from simulations. Abyan Khabir Irfan from Cleveland State University and Chansu Yu investigate this challenge using the Quantum Approximate Optimization Algorithm, or QAOA, a promising approach to solving complex problems. Their work explores how different optimisation techniques and error mitigation strategies perform when QAOA circuits run on actual quantum hardware, specifically the System One at the Cleveland Clinic, and compares these results to simulations. By meticulously analysing the impact of noise, this research provides crucial insights into the complexities of implementing QAOA on existing quantum systems and guides future efforts to build more robust and reliable quantum computers.

This research focused on solving the MaxCut problem, a classical optimization challenge where the goal is to divide a graph’s nodes to maximize the number of edges connecting different groups. The team demonstrated that optimization methods such as COBYLA and Conjugate Gradient effectively improved QAOA circuit performance, and that reducing circuit depth decreased computation time, although potentially at the cost of solution quality. Researchers systematically tested different minimization methods and variations in QAOA circuit depth to understand their impact on performance, incorporating various error mitigation techniques to reduce the effects of noise and improve solution accuracy.

Key differences were revealed between results obtained on simulators and those from actual quantum hardware, particularly in the parameter progression observed with the Powell method. Results demonstrate that the Conjugate Gradient method performs well on noisy quantum hardware, exhibiting distinct patterns in cost trajectory and parameter progression compared to simulations. Surprisingly, increasing the depth of the QAOA circuit did not yield improved performance under the tested conditions. However, the team observed positive results when applying error mitigation methods, demonstrating their potential to enhance the accuracy of QAOA on real quantum hardware. This system, featuring a 127-qubit IBM Eagle R3 processor, achieves a coherence time exceeding 50 microseconds, single-qubit gate errors below 0. 5%, two-qubit gate errors under 2. 5%, and measurement errors below 5%. The research focused on solving the Max-Cut problem, a classical optimization challenge where the goal is to divide a graph’s nodes to maximize the number of edges connecting different groups.

Researchers utilized a pre-existing code base as the foundation for their implementation and systematically compared several key parameters and techniques. They tested three distinct minimization methods, COBYLA, Powell, and Conjugate Gradient, to optimize the QAOA circuits, and varied the depth of the QAOA circuit to explore its impact on performance. Throughout the experiments, the team meticulously tracked solution quality and monitored the evolution of cost and parameter values during the optimization process. Results revealed that the Conjugate Gradient method performed well on the noisy quantum hardware, exhibiting distinct patterns in cost trajectory and parameter progression compared to the simulator.

Surprisingly, increasing the depth of the QAOA circuit did not yield improved performance under the tested conditions. However, the team observed positive results when applying error mitigation methods, demonstrating their potential to enhance the accuracy of QAOA on real quantum hardware. 5%, two-qubit gate errors under 2. 5%, and measurement errors below 5%. This high-performance system enabled detailed analysis of QAOA’s behavior under realistic conditions.

Experiments focused on solving the Max-Cut problem, a classical optimization challenge where the goal is to divide a graph’s nodes to maximize the edges connecting different groups. Researchers meticulously tracked solution quality and monitored the evolution of cost and parameter values throughout the optimization process. They systematically tested different minimization methods, including COBYLA, Powell, and Conjugate Gradient, alongside variations in QAOA circuit depth, and explored various QAOA variants. Results demonstrate that the Conjugate Gradient method performs effectively on noisy hardware, exhibiting distinct patterns in cost trajectory and parameter progression compared to simulations.

Surprisingly, increasing the QAOA circuit depth did not yield performance improvements under the tested experimental conditions. However, the team observed positive results when implementing pulse-based error mitigation methods, which demonstrably improved solution quality on the quantum hardware. These findings highlight the complex interplay between algorithm design, minimization techniques, and error mitigation strategies in achieving optimal performance on near-term quantum devices. The team demonstrated that optimization methods such as COBYLA and Conjugate Gradient effectively improved QAOA circuit performance within the experimental setup, and that reducing circuit depth decreased computation time, although potentially at the cost of solution quality. The experiments incorporated various error mitigation techniques, including Pauli twirling, dynamic decoupling, and transpiler optimizations, alongside a commercial platform, demonstrating the viability of hybrid workflows where optimization occurs on simulators before circuit execution on hardware. The team showed that transparent, reproducible error mitigation methods can achieve results comparable to proprietary solutions, validating existing platforms while paving the way for more customizable approaches.

Acknowledging limitations, the authors note the need for further investigation into the discrepancies observed between simulations and hardware results. Future work will focus on a more detailed analysis of these differences, exploring additional optimization strategies and alternative circuit designs. The team also plans to leverage a benchmarking library to systematically evaluate QAOA performance on larger, more complex problems, ultimately aiming to improve QAOA execution on noisy quantum devices and better understand the impact of qubit connectivity.