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Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

Quantum Approximate Optimization Algorithm for MaxCut: A Qiskit-Based Implementation and Analysis

Mohammed Said Al Salti, Hafiz M. Asif

Published Aug 17, 2026• 0 citations
Publisher
DOI
10.1007/978-3-032-32862-5_1

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对于解决组合优化问题，标准量子近似优化算法（Quantum approximate optimization algorithm, QAOA）的可训练参数数量随着层数明显增长，在资源受限的有噪中等规模量子（Noisy intermediate-scale quantum, NISQ）环境下存在一定的局限性。为缓解这一问题，先前提出的多参数问题无关层增强QAOA （Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer, QAOA+）在层数为1的标准QAOA 后面引入一个链式结构的多参数问题无关层，通过增加额外的耦合和可调参数来扩展可达态空间。受原始QAOA+ 启发，本文提出了一种新颖的改进QAOA+ ，即全联通QAOA+ （Fully-Connected QAOA+, FC-QAOA+）。 FC-QAOA+ 由层数为1的标准QAOA 、全联通多参数问题无关层和测量层构成。全联通多参数问题无关层将原始QAOA+ 的问题无关层的耦合拓扑从链式拓展为全联通，即问题无关层允许任意两比特进行相互作用（总数达到n(n-1)/2 对，其中n为输入量子比特数），在单一增强层内显著扩大可达态空间。对于边概率为0.8的随机图、完全图、2-正则图、4-正则图这些加权图上的最大切割（Maximum Cut, MaxCut）问题，在层数都为1且图的节点数属于[4,11]时，基于IBM Qiskit 平台的仿真实验表明：（1）在不同节点数上FC-QAOA+ 的平均逼近率与多角度量子近似优化算法（Multi-angle quantum approximate optimization algorithm, MA-QAOA）的平均逼近率各有优劣；（2）在所有节点数上，FC-QAOA+ 的平均逼近率优于标准QAOA 、RY 层辅助量子近似优化算法（RY-layer-assisted quantum approximate optimization algorithm, RY-QAOA）和原始QAOA+ ；（3）FC-QAOA+ 在节点数较少时的平均逼近率会更容易接近于1。

Zhongguo kexue. Wulixue Lixue Tianwenxue•Dec 19, 2025•0 citations
Quantum algorithms can be used to perform unsupervised machine learning tasks like data clustering by mapping the distance between data points to a graph optimization problem (i.e. MAXCUT) and finding optimal solution through energy minimization using hybrid quantum classical methods. Taking advantage of the IBM runtime environment, we benchmark the performance of the "Warm-Start" (ws) variant of Quantum Approximate Optimization Algorithm (QAOA) versus the standard implementation of QAOA and the variational quantum eigensolver (VQE) for unstructured clustering problems using real world dataset with respect to accuracy and execution time. Our numerical results show a strong speedup in execution time for different optimization algorithms using the IBM Qiskit Runtime architecture and increased speedup in classification accuracy in ws-QAOA algorithm
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.
对于解决组合优化问题，标准量子近似优化算法（Quantum approximate optimization algorithm, QAOA）的可训练参数数量随着层数明显增长，在资源受限的有噪中等规模量子（Noisy intermediate-scale quantum, NISQ）环境下存在一定的局限性。为缓解这一问题，先前提出的多参数问题无关层增强QAOA （Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer, QAOA+）在层数为1的标准QAOA 后面引入一个链式结构的多参数问题无关层，通过增加额外的耦合和可调参数来扩展可达态空间。受原始QAOA+ 启发，本文提出了一种新颖的改进QAOA+ ，即全联通QAOA+ （Fully-Connected QAOA+, FC-QAOA+）。 FC-QAOA+ 由层数为1的标准QAOA 、全联通多参数问题无关层和测量层构成。全联通多参数问题无关层将原始QAOA+ 的问题无关层的耦合拓扑从链式拓展为全联通，即问题无关层允许任意两比特进行相互作用（总数达到n(n-1)/2 对，其中n为输入量子比特数），在单一增强层内显著扩大可达态空间。对于边概率为0.8的随机图、完全图、2-正则图、4-正则图这些加权图上的最大切割（Maximum Cut, MaxCut）问题，在层数都为1且图的节点数属于[4,11]时，基于IBM Qiskit 平台的仿真实验表明：（1）在不同节点数上FC-QAOA+ 的平均逼近率与多角度量子近似优化算法（Multi-angle quantum approximate optimization algorithm, MA-QAOA）的平均逼近率各有优劣；（2）在所有节点数上，FC-QAOA+ 的平均逼近率优于标准QAOA 、RY 层辅助量子近似优化算法（RY-layer-assisted quantum approximate optimization algorithm, RY-QAOA）和原始QAOA+ ；（3）FC-QAOA+ 在节点数较少时的平均逼近率会更容易接近于1。