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IEEE International Conference on Quantum Computing and Engineering (QCE)

Parameter Transferability in QAOA Under Noisy Conditions

Quinn Langfitt, Jose Falla, Ilya Safro, Yuri Alexeev

Published Sep 17, 2023• 1 citation
Publisher

Abstract

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.

DOI
10.1109/qce57702.2023.10252

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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.
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization problem is achieved by preparing a quantum state through the optimization of quantum circuit parameters. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. In this work we show clustering of optimal QAOA parameters around specific values; consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). We apply this approach to several instances of random graphs with a varying number of nodes as well as parity and show that one can use optimal donor graph QAOA parameters as near-optimal parameters for larger acceptor graphs with comparable approximation ratios. This work presents a pathway to identifying classes of combinatorial optimization instances for which variational quantum algorithms such as QAOA can be substantially accelerated.
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization problem is achieved by preparing a quantum state through the optimization of quantum circuit parameters. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. In this work we show clustering of optimal QAOA parameters around specific values; consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). We apply this approach to several instances of random graphs with a varying number of nodes as well as parity and show that one can use optimal donor graph QAOA parameters as near-optimal parameters for larger acceptor graphs with comparable approximation ratios. This work presents a pathway to identifying classes of combinatorial optimization instances for which variational quantum algorithms such as QAOA can be substantially accelerated.
The Quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. In a typical QAOA setup, a set of quantum circuit parameters is optimized to prepare a quantum state used to find the optimal solution of a combinatorial optimization problem. Several empirical observations about optimal parameter concentration effects for special QAOA MaxCut problem instances have been made in recent literature, however, a rigorous study of the subject is still lacking. We show that convergence of the optimal QAOA parameters around specific values and, consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on the local properties of the graphs, specifically the types of subgraphs (lightcones) from which the graphs are composed. We apply this approach to random regular and general random graphs. For example, we demonstrate how optimized parameters calculated for a 6-node random graph can be successfully used without modification as nearly optimal parameters for a 64-node random graph, with less than 1% reduction in approximation ratio as a result. This work presents a pathway to identifying classes of combinatorial optimization instances for which such variational quantum algorithms as QAOA can be substantially accelerated.
Abstract The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. Due to clustering of optimal QAOA parameters for MaxCut, successful parameter transferability between different MaxCut instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). In this work, we apply five different graph embedding techniques to determine good donor candidates for parameter transferability, including parameter transferability between different classes of MaxCut instances. Using this technique, we effectively reduce the number of iterations required for parameter optimization, obtaining an approximate solution to the target problem with an order of magnitude speedup. This procedure also effectively removes the problem of encountering barren plateaus during the variational optimization of parameters. Additionally, our findings demonstrate that the transferred parameters maintain effectiveness when subjected to noise, supporting their use in real-world quantum applications. This work presents a framework for identifying classes of combinatorial optimization instances for which optimal donor candidates can be predicted such that QAOA can be substantially accelerated under both ideal and noisy conditions.
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.