Abstract The quantum approximate optimization algorithm (QAOA) is a promising approach for solving combinatorial optimization problems on real quantum devices. As QAOA scales to tackle larger problem instances, the limited qubit capacity of single-chip systems becomes a critical bottleneck. To overcome this limitation, distributed quantum computing (DQC) provides a scalable solution. However, when QAOA circuits are executed in such systems, their performance is significantly hindered by the high cost of remote communication. Motivated by this challenge, we propose HiQ - DF , a QAOA circuit design framework tailored for DQC systems. By employing a hierarchical optimization strategy, HiQ - DF enables comprehensive multi-objective optimization during circuit construction. Experimental results on QAOA circuits solving MaxCut instances show that our framework significantly outperforms baseline methods, achieving an average reduction of 26.12% in EPR pair usage (up to 36.85%), 26.44% in circuit latency (up to 35.27%), and 39.63% in circuit depth (up to 49.3%).
Abstract The quantum approximate optimization algorithm (QAOA) is a promising approach for solving combinatorial optimization problems on real quantum devices. As QAOA scales to tackle larger problem instances, the limited qubit capacity of single-chip systems becomes a critical bottleneck. To overcome this limitation, distributed quantum computing (DQC) provides a scalable solution. However, when QAOA circuits are executed in such systems, their performance is significantly hindered by the high cost of remote communication. Motivated by this challenge, we propose HiQ - DF , a QAOA circuit design framework tailored for DQC systems. By employing a hierarchical optimization strategy, HiQ - DF enables comprehensive multi-objective optimization during circuit construction. Experimental results on QAOA circuits solving MaxCut instances show that our framework significantly outperforms baseline methods, achieving an average reduction of 26.12% in EPR pair usage (up to 36.85%), 26.44% in circuit latency (up to 35.27%), and 39.63% in circuit depth (up to 49.3%).
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.
Quantum data-center (QDC) architectures aim to scale distributed quantum computing (DQC) by interconnecting multiple quantum processing units (QPUs), but their performance depends strongly on how algorithmic communication patterns interact with entanglement generation, switch reconfiguration, and network topology. This paper studies the Quantum Approximate Optimization Algorithm (QAOA) as a graph-structured optimization workload for QDC-based distributed quantum computing. We adapt QAOA to SwitchQNet, a distributed quantum compiler framework that schedules communication and entanglement generation over switch-based QDC networks, by adding a routing generator that converts graph-dependent two-qubit cost interactions into remote-CX communication requests across QPUs. Using this extension, we evaluate QAOA instances across Clos, fat-tree, and spine-leaf topologies, measuring communication latency, EPR-pair overhead, EPR wait time, retry overhead, and sensitivity to buffer size, look-ahead depth, communication-qubit count, EPR latency, and EPR fidelity assumptions. The results show that QAOA obtains modest but consistent latency reductions, highlighting its value as a diagnostic benchmark for studying the interaction between algorithm structure, entanglement management, and quantum-network architecture.
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.
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.
Maximum cut (Max-Cut) problem is one of the most important combinatorial optimization problems because of its various applications in real life, and recently Quantum Approximate Optimization Algorithm (QAOA) has been widely employed to solve it. However, as the size of the problem increases, the number of qubits required will become larger. With the aim of saving qubits, we propose a coupling framework for designing QAOA circuits to solve larger-scale Max-Cut problem. This framework relies on a classical algorithm that approximately solves a certain variant of Max-Cut, and we derive an approximation guarantee theoretically, assuming the approximation ratio of the classical algorithm and QAOA. Furthermore we design a heuristic approach that fits in our framework and perform sufficient numerical experiments, where we solve Max-Cut on various 24-vertex Erdős-Rényi graphs. Our framework only consumes 18 qubits and achieves 0.9950 approximation ratio on average, which outperforms the previous methods showing 0.9778 (quantum algorithm using the same number of qubits) and 0.9643 (classical algorithm). The experimental results indicate our well-designed quantum-classical coupling framework gives satisfactory approximation ratio while reduces the qubit cost, which sheds light on more potential computing power of NISQ devices.
The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for solving NP hard combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) hardware. However, its performance is critically dependent on the selection of the circuit depth a parameter that must be specified a priori without clear guidance. In this paper, we introduce a variant of QAOA called dynamic depth Quantum Approximate Optimization Algorithm (DDQAOA) that resolves the challenge of pre selecting a fixed circuit depth. Our method adaptively expands circuit depth, starting from p = 1 and progressing up to p = 10, by transferring learned parameters to deeper circuits based on convergence criteria. We tested this approach on 100 instances of the Constrained Shortest Path Problem (CSPP) at 10 qubit and 16 qubit scales. Our DDQAOA achieved superior approximation ratios and success probabilities with fewer CNOT gate evaluations than the standard QAOA for p = 3, 5, 10, and 15. In particular, while standard QAOA at p = 15 achieved results close to our approach, it used 217% and 159.3% more CNOT gates for 10 qubit and 16 qubit instances, respectively. This demonstrates the performance and practical applicability of DDQAOA to solve combinatorial optimization problems on near term devices.