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IEEE International Conference on Quantum Computing and Engineering (QCE)

Simulations of Quantum Approximate Optimization Algorithm on HPC-QC Integrated Systems

Seongmin Kim, In‐Saeng Suh

Published Sep 15, 2024• 3 citations
Publisher

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.

DOI
10.1109/qce60285.2024.10357

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The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.
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Quantum computers are expected to offer advantages in solving optimization problems challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class of problems with relevance in finance and logistics. The Quantum Approximate Optimization Algorithm (QAOA) is a prominent candidate for solving QUBO problems on near-term quantum devices. In this paper, we evaluate the performance of both the standard QAOA and the adaptive derivative assembled problem tailored QAOA (ADAPT-QAOA) to solve QUBO problems of varying sizes and hardnesses for financial feature selection problems. Our main observation is that ADAPT-QAOA achieves substantially higher approximation ratios than standard QAOA for harder feature-selection problems (α = 0.6) with statistically significant improvements observed for problem sizes n = 6 and 14. However, the standard QAOA remains competitive for simpler problems. Additionally, we evaluate the practical feasibility and limitations of QAOA through a hardware-aware scaling analysis based on the real-device calibration data for various hardware platforms. We estimate that standard QAOA implementation on superconducting quantum computers provides a shorter time-to-solution compared to trapped-ion devices, while trapped-ion devices yield more favorable error rates. Our findings provide a comprehensive overview of the challenges, trade-offs, and strategies for deploying QAOA-based methods on near-term quantum hardware.
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This study explores quantum computing for combinatorial optimization, focusing on the Traveling Salesman Problem (TSP). Using Qiskit, the Quantum Approximate Optimization Algorithm (QAOA) is implemented on simulators and quantum hardware, and compared with classical optimization using Gurobi. TSP instances are encoded as Quadratic Unconstrained Binary Optimization (QUBO) problems derived from the Miller–Tucker–Zemlin formulation, with quadratic penalties enforcing degree and subtour constraints. Results indicate that QAOA consistently generates feasible tours, but classical branch-and-bound methods achieve better solution quality and runtime. On Noisy Intermediate-Scale Quantum (NISQ) devices, performance degrades with problem size due to sensitivity to parameter tuning, penalty scaling, and hardware noise. Among the tested classical optimizers, COBYLA provides the best balance of efficiency and noise tolerance. Overall, this work establishes a reproducible quantum-classical workflow, provides performance baselines, and identifies critical factors such as encoding design, optimizer choice, and error mitigation for improving near-term quantum heuristic performance.
Quantum computing holds great potential to accelerate the process of solving complex combinatorial optimization problems. The Distributed Quantum Approximate Optimization Algorithm (DQAOA) addresses high-dimensional, dense problems using current quantum computing techniques and high-performance computing (HPC) systems. In this work, we improve the scalability and efficiency of DQAOA through advanced problem decomposition and parallel execution using message passing on the Frontier CPU/GPU supercomputer. Our approach ensures efficient quantum-classical workload management by distributing large problem instances across classical and quantum resources. Experimental results demonstrate that enhanced decomposition strategies and GPU-accelerated quantum simulations significantly improve DQAOA's performance, achieving up to 10x speedup over CPU-based simulations. This advancement enables better scalability for large problem instances, supporting the practical deployment of GPU systems for hybrid quantum-classical applications. We also highlight ongoing integration efforts using the Quantum Framework (QFw) to support future HPC-quantum computing systems.