article · Scientific Reports
The Quantum Approximate Optimisation Algorithm (QAOA) is designed for near-term intermediate-scale quantum devices to solve combinatorial optimisation problems by combining a quantum circuit with a classical optimiser. This research evaluates how realistic noise influences the classical optimiser and circuit depth in QAOA implementations. While classical optimisers perform similarly in ideal, noise-free state vector simulations, differences appear under noisy conditions. When subjected to shot noise, the Adam and AMSGrad optimisers perform best. Under realistic hardware noise, SPSA, Adam, and AMSGrad achieve the strongest results. Furthermore, tests on five-qubit minimum vertex cover problems demonstrate that solution quality improves as circuit depth increases up to roughly six layers. Beyond this point, solution quality degrades. The findings indicate that adding circuit layers to enhance accuracy can become counterproductive on noisy quantum hardware.
Today's quantum computers are prone to hardware noise, which hinders their ability to solve complex calculations reliably. By identifying the most resilient classical optimisers and establishing limits on circuit depth, this work helps quantum software developers design more efficient algorithms tailored to the physical limitations of current quantum machines.
This work is relevant to quantum software developers and algorithm designers seeking to implement combinatorial optimisation tools on near-term intermediate-scale quantum hardware. It provides practical guidance for tuning algorithm parameters to mitigate hardware noise. However, tested only on small five-qubit problem sets, the research represents early-stage technical evaluation rather than a market-ready deployment.
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The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) providing approximate solutions for combinatorial optimization problems. The QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a classical optimizer, to minimize some cost function, computed on the quantum device. This paper presents an investigation into the impact of realistic noise on the classical optimizer and the determination of optimal circuit depth for the Quantum Approximate Optimization Algorithm (QAOA) in the presence of noise. We find that, while there is no significant difference in the performance of classical optimizers in a state vector simulation, the Adam and AMSGrad optimizers perform best in the presence of shot noise. Under the conditions of real noise, the SPSA optimizer, along with ADAM and AMSGrad, emerge as the top performers. The study also reveals that the quality of solutions to some 5 qubit minimum vertex cover problems increases for up to around six layers in the QAOA circuit, after which it begins to decline. This analysis shows that increasing the number of layers in the QAOA in an attempt to increase accuracy may not work well in a noisy device.
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DOI: 10.1038/s41598-024-66625-6
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