Abstract Quantum algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices require optimization strategies matched to circuit structure. We present two complementary approaches: VERMICULAR, achieving 93.0% success rates for Grover’s algorithm through strategic dynamical decoupling (DD) placement (vs. 18.3% baseline), and systematic QAOA parameter optimization achieving 94.5% approximation ratios for MaxCut (vs. 39.6% with theoretical parameters). Through >15,000 circuit executions across IQM Garnet, Rigetti Ankaa-3, and IonQ Forte-1 (total cost: €70), we demonstrate that circuit structure determines which strategy succeeds: DD helps algorithms with substantial idle time (Grover: 34% idle → 5× improvement) but degrades continuously-active circuits (QAOA: 2.4% idle → 50% degradation with DD). We systematically characterize algorithm noise resilience via critical noise thresholds (σc), finding Bell states achieve 4× higher σc than product states (0.200 vs 0.050, p < 0.001) and that σc predicts hardware performance (r = 0.94, p = 0.006). QAOA scaling studies (3-40 qubits) reveal exponential decay with 56% plateau beyond 20 qubits. Simulator-optimized parameters transfer effectively to hardware (85-98% efficiency), but hardware-to-hardware transfer requires architecture-specific tuning. We provide SigmaCSuite, an open-source validation framework, and complete experimental protocols. These findings establish that optimization strategy must match circuit structure: idle-time protection for search algorithms, parameter tuning for variational algorithms—achieving 2.5-5× improvements through targeted approaches.
Abstract Quantum algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices require optimization strategies matched to circuit structure. We present two complementary approaches: VERMICULAR, achieving 93.0% success rates for Grover’s algorithm through strategic dynamical decoupling (DD) placement (vs. 18.3% baseline), and systematic QAOA parameter optimization achieving 94.5% approximation ratios for MaxCut (vs. 39.6% with theoretical parameters). Through >15,000 circuit executions across IQM Garnet, Rigetti Ankaa-3, and IonQ Forte-1 (total cost: €70), we demonstrate that circuit structure determines which strategy succeeds: DD helps algorithms with substantial idle time (Grover: 34% idle → 5× improvement) but degrades continuously-active circuits (QAOA: 2.4% idle → 50% degradation with DD). We systematically characterize algorithm noise resilience via critical noise thresholds (σc), finding Bell states achieve 4× higher σc than product states (0.200 vs 0.050, p < 0.001) and that σc predicts hardware performance (r = 0.94, p = 0.006). QAOA scaling studies (3-40 qubits) reveal exponential decay with 56% plateau beyond 20 qubits. Simulator-optimized parameters transfer effectively to hardware (85-98% efficiency), but hardware-to-hardware transfer requires architecture-specific tuning. We provide SigmaCSuite, an open-source validation framework, and complete experimental protocols. These findings establish that optimization strategy must match circuit structure: idle-time protection for search algorithms, parameter tuning for variational algorithms—achieving 2.5-5× improvements through targeted approaches.
The performance of quantum algorithms on near-term devices is heavily constrained by hardware noise, yet systematic comparisons of algorithmic vulnerability across diverse noise types remain limited. In this study, we benchmark three representative algorithms: quantum teleportation, Grover’s search, and the Quantum Approximate Optimization Algorithm (QAOA), under depolarizing, amplitude damping, phase damping, and thermal relaxation channels. Using exact density-matrix simulations, we characterize algorithmic performance by evaluating state fidelity decay as a function of noise strength. To enable fair, structure-aware comparisons across circuits of varying depths, we introduce a novel metric, the per-gate decay rate. Our analysis reveals that teleportation exhibits the lowest per-gate vulnerability, whereas Grover’s algorithm demonstrates substantially larger, super-linear decay driven by its repeated oracle–diffuser architecture. QAOA displays intermediate and stable noise resilience across system sizes. Finally, we validate our simulation framework through hardware experiments on an IBM Heron processor, demonstrating strong agreement with theoretical predictions (Pearson’s correlation coefficient r = 0.981). This work establishes a quantitative, structure-aware framework for assessing circuit-level noise sensitivity and offers actionable insights for algorithm selection in the noisy intermediate-scale quantum era.
The Quantum Approximate Optimization Algorithm (QAOA) is widely regarded as a promising near-term quantum algorithm for addressing hard combinatorial optimization problems on Noisy Intermediate-Scale Quantum (NISQ) devices; however, its real-world effectiveness is severely constrained by hardware noise, including gate infidelities, decoherence, and measurement errors. This work explores an error mitigation–driven approach to enhance the performance and robustness of QAOA without altering its algorithmic structure or requiring fault-tolerant quantum resources. Measurement error mitigation and zero-noise extrapolation are incorporated into the execution and post-processing stages of QAOA circuits and evaluated using the Minimum Vertex Cover problem as a representative benchmark. Performance is assessed through approximation ratios, solution stability, and noise sensitivity across multiple circuit depths. The results indicate that error mitigation not only improves approximation accuracy but also stabilizes output distributions and delays performance degradation at increased circuit depths. Additionally, the mitigated executions demonstrate better consistency across repeated runs, highlighting improved resilience to stochastic noise. These findings emphasize that lightweight and hardware-efficient error mitigation techniques can significantly extend the practical usability of QAOA on current NISQ hardware, providing a scalable and realistic pathway for executing quantum optimization algorithms more reliably in near-term quantum computing environments.
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 leading candidate for solving combinatorial optimization problems on near-term quantum hardware. However, its practical deployment remains severely limited by hardware-induced noise and decoherence. In the absence of full fault tolerance, Quantum Error Mitigation (QEM) techniques offer a viable approach to enhance QAOA performance on noisy intermediate-scale quantum (NISQ) devices. In this work, we present a unified classification of QEM strategies specifically tailored for QAOA, systematically categorized into preprocessing, during execution, and post-processing phases. We further classify QAOA deployment settings—such as hardware-constrained devices, stochastic noise-dominated environments, and dense graphs problem—and recommend appropriate QEM techniques for each. A comparative analysis highlights the trade-offs among mitigation accuracy, resource overhead, and robustness to different noise types. By synthesizing recent advances and identifying open challenges, our paper provides both a comprehensive survey and a practical framework for designing robust, noise-resilient QAOA pipelines on near-term quantum platforms.
Large-scale combinatorial and continuous optimisation problems remain intractable for classical algorithms as problem dimensionality scales. Quantum computing offers advantages through parallelism, amplitude amplification, and tunnelling, but practical realisation on near-term noisy intermediate-scale quantum (NISQ) devices demands careful algorithm design balancing advantage against noise resilience and circuit depth constraints. This paper presents the Quantum Optimisation Algorithm Suite (QOAS), a systematic framework across four algorithmic paradigms: Adaptive QAOA with dynamic depth scheduling; Variational Quantum Eigensolver (VQE) for QUBO problems; hybrid Quantum Annealing (QA); and Grover-enhanced Branch and Bound (GBB) for constrained integer programming. QOAS is benchmarked on five problem classes (MaxCut, TSP, Portfolio, Drug-Target, Feature Selection) across n = 12-84 qubits on IBM Quantum Eagle (127-qubit) and Falcon (27-qubit). Adaptive QAOA achieves approximation ratio 0.924 (SD = 0.018) for MaxCut at n = 48 -- outperforming standard QAOA (0.848) and Goemans-Williamson (0.878) at equivalent wall-clock time. GBB achieves 28.4x speedup over classical branch-and-bound for the n = 24 drug-target problem. QOAS provides systematic methodology for algorithm selection, circuit depth optimisation, and noise mitigation for NISQ workloads.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices are near-term quantum computing devices that inherently suffer from imperfect gate implementation, decoherence, and measurement noise. The main type of variational quantum algorithms(VQAs) is based on Parameterized Quantum Circuits (PQCs), which, however, face practical challenges due to optimization instability of optimization caused by noise and reduced performance. In this paper, we suggest a comprehensive noise-resilient optimization framework for PQCs, which explicitly incorporates noise-resilient circuit architecture design, incorporating noise-aware training strategies into the variational optimization loop. The framework uses circuit structures that are efficient in depth and are hardware compatible in addition to adaptive optimizer choice, stochastic optimization, and averaging as a part of repeated measurement to reduce the impacts of realistic noise. Large-scale experiments are performed with different amounts of qubits, depths of the circuit and noise strengths with realistic noise models. The findings indicate that the convergence rate is faster, the stability is increased, the variability of run-to-run variability is minimized, and other robustness is better than the noise-unaware optimization techniques. Moreover, systematic studies determine optimal operating regions that optimally trade-off expressibility and noise tolerance to offer useful design advice on trusted implementation of VQAs with near-term quantum hardware.