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IEEE International Conference on Quantum Computing and Engineering (QCE)

Evaluating the Role of Noise Mitigation in QAOA: A Study of Zero-Noise Extrapolation and CVaR

Adriano Lusso, M. Vénere, Victor Onofre, Alberto Maldonado-Romo, J. A. Montañez-Barrera, Marco Domenico Santambrogio

Published Aug 30, 2025• 0 citations
Publisher

Abstract

In recent years, the Quantum Approximate Optimization Algorithm (QAOA) has attracted attention due to its potential to find good-quality solutions to combinatorial optimization problems. In QAOA, there is a set of parameters that are usually tuned using classical optimization methods. These methods search for parameters that identify good solutions to the given problems. Yet, the effects of noise on current Noisy Intermediate-Scale Quantum (NISQ) devices proved to have a destructive impact on the search of such parameters, reducing the quality of the exploration and producing inefficient solutions. In this work, we explore the Zero-Noise Extrapolation (ZNE) technique to mitigate the effects of noise in QAOA, the modification of the objective function using the Conditional Value at Risk (CVaR), and present simulations using both methods on different MaxCut instances. We found that ZNE, in combination with CVar, slightly restores the noisy energy landscape of QAOA, improving the optimal energy found. However, this is not the case when measuring high-quality solutions. While CVaR slightly improves solution quality, ZNE interferes with these results. Finally, we provide an open-source integration of ZNE and CVar, to support researchers in assessing the performance of their QAOA workflows in noisy environments, towards effective applications of QAOA.

DOI
10.1109/qce65121.2025.10466

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In recent years, the Quantum Approximate Optimization Algorithm (QAOA) has attracted attention due to its potential to find good-quality solutions to combinatorial optimization problems. In QAOA, there is a set of parameters that are usually tuned using classical optimization methods. These methods search for parameters that identify good solutions to the given problems. Yet, the effects of noise on current Noisy Intermediate-Scale Quantum (NISQ) devices proved to have a destructive impact on the search of such parameters, reducing the quality of the exploration and producing inefficient solutions. In this work, we explore the Zero-Noise Extrapolation (ZNE) technique to mitigate the effects of noise in QAOA, the modification of the objective function using the Conditional Value at Risk (CVaR), and present simulations using both methods on different MaxCut instances. We found that ZNE, in combination with CVar, slightly restores the noisy energy landscape of QAOA, improving the optimal energy found. However, this is not the case when measuring high-quality solutions. While CVaR slightly improves solution quality, ZNE interferes with these results. Finally, we provide an open-source integration of ZNE and CVar, to support researchers in assessing the performance of their QAOA workflows in noisy environments, towards effective applications of QAOA.
The Quantum Approximate Optimization Algorithm (QAOA) is widely regarded as a promising near-term quantum algorithm for addressing hard combinatorial optimization problems on Noisy Intermediate-Scale Quantum (NISQ) devices; however, its real-world effectiveness is severely constrained by hardware noise, including gate infidelities, decoherence, and measurement errors. This work explores an error mitigation–driven approach to enhance the performance and robustness of QAOA without altering its algorithmic structure or requiring fault-tolerant quantum resources. Measurement error mitigation and zero-noise extrapolation are incorporated into the execution and post-processing stages of QAOA circuits and evaluated using the Minimum Vertex Cover problem as a representative benchmark. Performance is assessed through approximation ratios, solution stability, and noise sensitivity across multiple circuit depths. The results indicate that error mitigation not only improves approximation accuracy but also stabilizes output distributions and delays performance degradation at increased circuit depths. Additionally, the mitigated executions demonstrate better consistency across repeated runs, highlighting improved resilience to stochastic noise. These findings emphasize that lightweight and hardware-efficient error mitigation techniques can significantly extend the practical usability of QAOA on current NISQ hardware, providing a scalable and realistic pathway for executing quantum optimization algorithms more reliably in near-term quantum computing environments.
The quantum approximate optimization algorithm (QAOA) is widely recognized for its potential to deliver quantum advantage in combinatorial optimization tasks. As a hybrid classical-quantum algorithm, it achieves an approximate solution to the combinatorial optimization problem by preparing a specific quantum state via a classical optimization of the quantum circuit parameters. A key property of QAOA is the observed concentration and transferability of optimal parameters across distinct problem instances, linked to local graph characteristics such as subgraph types (lightcones) and node degrees (parity) [1]. However, quantum noise poses a critical challenge in the current NISQ era, hindering the performance of QAOA, particularly for large system sizes. In this follow-up study, we investigate the resilience of parameter transferability under noisy conditions. Leveraging zero-noise extrapolation (ZNE), we evaluate the transferability's robustness across various random graphs under different noise levels. Our analysis reveals that the transferability of optimal parameters from smaller ‘donor’ graphs to larger ‘acceptor’ graphs retains its effectiveness, even under substantial noise when combined with ZNE. Importantly, by illustrating that QAOA parameter transferability can still be exploited effectively among NISQ devices, we offer a pragmatic approach to enhance the algorithm's performance. Our research reinforces the promise of QAOA for large-scale applications under the practical challenges of quantum noise.
Variational quantum circuits (VQCs) are central to near-term quantum computing, yet their practical deployment is severely hindered by noise. While existing error mitigation methods, such as zero-noise extrapolation (ZNE), typically assume static noise, real noisy intermediate-scale quantum (NISQ) systems exhibit dynamic, time-varying noise that remains largely unaddressed. To overcome this critical gap, our work introduces a novel adaptive noise mitigation framework for VQCs that integrates ZNE with contextual multi-armed bandits (CMAB), enabling dynamic, context-aware selection of circuit-folding levels based on ansatz parameters (e.g., depth, parameter count) and the evolving noise environment. Unlike fixed-fold or heuristic ZNE, our approach uses online adaptation to improve the accuracy of ZNE and reduce redundant quantum circuit executions. Our extensive simulations and experiments on real quantum hardware reveal the following important properties: (i) deeper VQCs accumulate noise, degrading accuracy and increasing the number of quantum circuit executions; (ii) ZNE restores estimator fidelity when the folding level is chosen appropriately; and (iii) CMAB-guided folding cuts quantum circuit execution round trips by up to 40\%, bytes exchanged by up to 35\%, and end-to-end cost by up to 30\% under a 10~Mbps budget, with up to 6.9\% higher estimator fidelity (CIFAR-10, depth 3, noise band η=0.05η=0.05η=0.05), versus fixed-fold and grid-search ZNE. These results demonstrate substantial performance gains over existing noise mitigation methods, underscoring the effectiveness of our design in supporting robust noise mitigation for VQCs. The source code is also publicly released to support reproducibility.
Abstract In the noisy intermediate-scale quantum (NISQ) era, quantum approximate optimisation algorithms are important tools for solving NP-hard problems such as combinatorial optimisation. However, most QAOA implementations ignore the inherent noise in quantum circuit environments. This study proposes a noisy quantum approximate optimisation algorithm (NQAOA) and analyses its performance under noisy conditions through numerical simulations. We compare the approximate ratios (AR) of various graphs under different optimisation strategies and noise conditions, and assess the impact of circuit depth, node count, edge count, and noise coefficient on the maximum cut (MaxCut). Experimental results show that noise leads to overfitting, and the approximate ratio ( AR ) exhibits fluctuating changes as the edge count e increases. The AR values under ideal conditions and the expected results are both superior to those under noisy conditions. This study is the first to systematically integrate multiple types of quantum noise into the QAOA framework, quantitatively analysing the synergistic effects of noise type, optimiser performance, and graph structure. Through theoretical derivations and numerical simulations, we established linear/exponential theoretical boundaries for AR decay related to noise coefficients, providing a critical reference for designing noise-resistant quantum optimisation algorithms on NISQ devices.
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.