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.
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.
While combinatorial optimization problems are central to many scientific and engineering applications, their solution remains challenging due to exponentially large search spaces. Variational quantum algorithms offer a promising route for tackling such problems, yet their practical performance is limited by repeated quantum circuit evaluations and classical parameter updates. In this work, we introduce DQAOA-GPT, a hybrid framework that integrates the distributed quantum approximate optimization algorithm (DQAOA), which decomposes a large optimization problem into smaller sub-problems, with GPT-based quantum circuit generation for solving those sub-problems. Rather than relying on iterative variational optimization, the proposed approach uses a trained generative model to directly generate high-quality quantum circuits for the decomposed sub-problems. As a benchmark, we evaluate DQAOA-GPT against conventional DQAOA on dense HUBO optimization problems with up to 100 decision variables. The results demonstrate that DQAOA-GPT significantly reduces computational cost while maintaining competitive solution quality, with larger acceleration observed for larger sub-problem sizes. Although this work focuses on benchmark-scale validation, the framework provides a promising foundation for larger-scale combinatorial optimization in hybrid HPC-QC environments through increased GPU resources and parallel computing capability.
Abstract Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for high-dimensional problems due to the large number of qubits required and the complexity of deep circuits, limiting its scalability for real-world applications. In this study, we present a distributed QAOA (DQAOA), which leverages distributed computing strategies to decompose a large computational workload into smaller tasks that require fewer qubits and shallower circuits than are necessary to solve the original problem. These sub-problems are processed using a combination of high-performance and quantum computing resources. The global solution is iteratively updated by aggregating sub-solutions, allowing convergence toward the optimal solution. We demonstrate that DQAOA can handle considerably large-scale optimization problems (e.g., 1000-bit problem), achieving a high solution quality and short time-to-solution, outperforming existing strategies. Furthermore, we realize DQAOA on a quantum-centric supercomputing architecture, paving the way for practical applications of gate-based quantum computers in real-world optimization tasks. To extend DQAOA’s applicability to materials science, we further develop an active learning algorithm integrated with our DQAOA (AL-DQAOA), which involves machine learning, DQAOA, and active data production in an iterative loop. We successfully optimize photonic structures using AL-DQAOA, indicating that solving real-world optimization problems using gate-based quantum computing is feasible. We expect the proposed DQAOA to be applicable to a wide range of optimization problems and AL-DQAOA to find broader applications in material design.
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.
This paper introduces a noise-aware distributed Quantum Approximate Optimization Algorithm (QAOA) tailored for execution on near-term quantum hardware. Leveraging a distributed framework, we address the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, which are hindered by limited qubit counts and high error rates. Our approach decomposes large QAOA problems into smaller subproblems, distributing them across multiple Quantum Processing Units (QPUs) to enhance scalability and performance. The noise-aware strategy incorporates error mitigation techniques to optimize qubit fidelity and gate operations, ensuring reliable quantum computations. We evaluate the efficacy of our framework using the HamilToniQ Benchmarking Toolkit, which quantifies the performance across various quantum hardware configurations. The results demonstrate that our distributed QAOA framework achieves significant improvements in computational speed and accuracy, showcasing its potential to solve complex optimization problems efficiently in the NISQ era. This work sets the stage for advanced algorithmic strategies and practical quantum system enhancements, contributing to the broader goal of achieving quantum advantage.
Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.
Many large-scale optimisation problems, such as those in power systems, finance and logistics can be potentially solved in the fundamentally new approach of quantum algorithms, namely Quantum Approximate Optimisation Algorithm (QAOA). In the context of fuzzy systems for instance, it is already shown that some of the intense computation associated with complex or higher-order fuzzy logic systems can be offloaded to such quantum algorithms. While the quantum computation hardware technology is still in its infancy, efficient simulations of the quantum algorithms play a crucial role in advancing quantum algorithms. The current CPU/GPU-based approaches suffer from high energy consumption and speed and scalability limitations. This paper presents the current position of our research to develop an efficient and scalable QAOA simulation based on a large network of Field-Programmable Gate Array (FPGA) modules, inspired by FPGA’s hardware-level parallelism. Although there exist a few attempts on using FPGA for general quantum circuits simulation, this project introduces a novel approach by employing a highly efficient recursive matrix decomposition algorithms specifically designed for QAOA. This work can pave the pathway a scalable and energy-efficient solution for cross-domain optimisation problems. The actual results and evaluations are to be reported in follow-up publications.