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IEEE Electron Devices Technology & Manufacturing Conference (EDTM)

Performance Comparison for Quantum Approximate Optimization Algorithm (QAOA) across Noiseless Simulation, Experimentally Benchmarked Noisy Simulation, and Experimental Hardware Platforms

Sanyam Singhal, Vandit Srivastava, P Rohith, Prateek Jain, Debanjan Bhowmik

Published Mar 3, 2024• 3 citations
Publisher

Abstract

We implement Quantum Approximate Optimization Algorithm (QAOA) on NP-Hard problem MaxCut (for 3-chain and 4-node chain graphs, and 4-node and 6node Mobius Ladder graphs) on a quantum simulator without noise, a simulator with experimentally bench-marked noise (fake back-end), and 5-qubit and 7-qubit processors. We use the following modes of operation: QAOA parameters updated through forward pass on the quantum circuit, modelled by the noiseless simulator as well as fake back-end, and the quantum circuit for final run with updated parameters implemented on the noiseless simulator, fake back-end, and real quantum processors. While QAOA yields higher approximation ratio compared to random guess for almost all graph instances, we also conclude that given the noise in existing quantum hardware, a quantum circuit with more than two stages is not suitable for experimental implementation of QAOA currently.

DOI
10.1109/edtm58488.2024.10512142

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Multi-angle quantum approximate optimization algorithm (ma-QAOA) has been proposed as an alternative to regular QAOA for solving optimization problems using noisy intermediate scale quantum (NISQ) hardware. Here, we first implement QAOA and ma-QAOA algorithms to solve MaxCut on weighted and unweighted versions of the Erdős–Rényi (ER) and random cubic (RC) graphs of 6 and 10 nodes. Quantum circuit parameters are updated iteratively through classical feedback with the quantum circuit for forward pass modelled on Qiskit simulator without noise models. Then, the quantum circuit for the final run with updated parameters is implemented on Qiskit simulator without noise models, Qiskit simulator with experimentally benchmarked noise models (fake back-end), and also on actual experimental quantum hardware (IBM’s 127-qubit quantum processor ibm brisbane). We show that for most graph instances, ma-QAOA performs better than QAOA (in terms of approximation ratio (AR)) and needs less stages in the quantum circuit for all three aforementioned methods. Finally, we extend our results up to 14-node RC graphs while restricting ourselves to Qiskit simulation without noise (both for parameter update and final run) and show that for most instances, ma-QAOA again needs much less stages compared to QAOA to obtain reasonable AR.

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This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.

•May 6, 2026•0 citations
We implement Quantum Approximate Optimization Algorithm (QAOA) on NP-Hard problem MaxCut (for 3-chain and 4-node chain graphs, and 4-node and 6node Mobius Ladder graphs) on a quantum simulator without noise, a simulator with experimentally bench-marked noise (fake back-end), and 5-qubit and 7-qubit processors. We use the following modes of operation: QAOA parameters updated through forward pass on the quantum circuit, modelled by the noiseless simulator as well as fake back-end, and the quantum circuit for final run with updated parameters implemented on the noiseless simulator, fake back-end, and real quantum processors. While QAOA yields higher approximation ratio compared to random guess for almost all graph instances, we also conclude that given the noise in existing quantum hardware, a quantum circuit with more than two stages is not suitable for experimental implementation of QAOA currently.
Multi-angle quantum approximate optimization algorithm (ma-QAOA) has been proposed as an alternative to regular QAOA for solving optimization problems using noisy intermediate scale quantum (NISQ) hardware. Here, we first implement QAOA and ma-QAOA algorithms to solve MaxCut on weighted and unweighted versions of the Erdős–Rényi (ER) and random cubic (RC) graphs of 6 and 10 nodes. Quantum circuit parameters are updated iteratively through classical feedback with the quantum circuit for forward pass modelled on Qiskit simulator without noise models. Then, the quantum circuit for the final run with updated parameters is implemented on Qiskit simulator without noise models, Qiskit simulator with experimentally benchmarked noise models (fake back-end), and also on actual experimental quantum hardware (IBM’s 127-qubit quantum processor ibm brisbane). We show that for most graph instances, ma-QAOA performs better than QAOA (in terms of approximation ratio (AR)) and needs less stages in the quantum circuit for all three aforementioned methods. Finally, we extend our results up to 14-node RC graphs while restricting ourselves to Qiskit simulation without noise (both for parameter update and final run) and show that for most instances, ma-QAOA again needs much less stages compared to QAOA to obtain reasonable AR.
Quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve NP-hard problems in near-term gate-based noisy quantum devices. In QAOA, the gate parameters of a parameterized quantum circuit (PQC) are varied by a classical optimizer to generate a quantum state with a significant support to the optimal solution. The existing analysis fails to consider nonidealities in the qubit quality i.e., short lifetime and imperfect gate operations in a realistic quantum hardware. In this article, we study the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analysis indicates that QAOA performance is noise-sensitive (especially higher-depth QAOA instances). Therefore, the optimal number of stages (p-value) for any QAOA instance is limited by the noise in the target hardware as opposed to the current perception that QAOA will provide monotonically better performance with higher-depth. We show that the two-qubit gate error has to be decreased by more than 75% of the current state-of-the-art levels to attain a performance within 10% of the maximum value for the lowest-depth QAOA.
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 promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.
The transition from theoretical quantum computing to practical real-world applications heavily relies onhybrid quantum-classical architectures designed for NoisyIntermediate-Scale Quantum (NISQ) devices. Among these approaches, the Quantum Approximate Optimization Algorithm(QAOA) is a prominent strategy for addressing complex combinatorial optimization challenges, such as the NP-hard MaxCut problem. Instead of performing the entire computationon a quantum processor, QAOA utilizes a quantum circuit toevaluate a parameterized cost function, whereas a classical optimizer refines the parameters iteratively. This study presentsa rigorous empirical evaluation comparing the performanceof QAOA against established classical solvers on small-scaleMax-Cut instances. All experiments were implemented andexecuted using Python (Qiskit Aer) on a state-vector simulator.Using Erdős–Rényi random graphs and regular graphs with4 to 20 nodes, we benchmark QAOA at depths p = 2 andp = 3 against simulated annealing, the Goemans–WilliamsonSDP-based algorithm, and a linear-time greedy heuristic. Ourexperimental results demonstrate that low-depth QAOA implementations exhibit severe performance degradation, prohibitive computational overhead (O(2^n) scaling), and low convergencerates compared to mature classical algorithms. At 20 nodes,QAOA (p = 2) achieves only a 0.467 approximation ratio versus0.856 for Goemans–Williamson, with a 210× runtime slowdownover greedy heuristics
This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.