In recent years, quantum computing has shown promise in solving certain problems more efficiently than classical methods. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a leading candidate for achieving quantum advantage on noisy intermediate-scale quantum (NISQ) devices. This study explores the application of QAOA to the Maximum Weighted Independent Set (MWIS) problem, with particular focus on circuit transpilation strategies and parameter optimization methods. Using IBM Qiskit, we systematically examine factors affecting QAOA performance, including different transpilation optimization levels and classical optimizer selection. Our results demonstrate that optimization level 3 reduced circuit depth by 32% compared to level 0 for p=3 circuits, while maintaining solution quality. Among classical optimizers, COBYLA achieved an 81.24% approximation ratio with only 54.8 function evaluations at p=2, outperforming both grid search and SPSA methods. Execution on IBM’s real quantum hardware resulted in performance degradation ranging from 16% at p=1 to 34% at p=3 compared to ideal simulations, highlighting the compounding impact of noise and gate errors as circuit depth increases.These findings provide practical guidance for quantum algorithm implementation on NISQ devices, demonstrating that appropriate selection of transpilation techniques and optimization methods can substantially improve quantum resource efficiency while maintaining solution quality.
In recent years, quantum computing has shown promise in solving certain problems more efficiently than classical methods. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a leading candidate for achieving quantum advantage on noisy intermediate-scale quantum (NISQ) devices. This study explores the application of QAOA to the Maximum Weighted Independent Set (MWIS) problem, with particular focus on circuit transpilation strategies and parameter optimization methods. Using IBM Qiskit, we systematically examine factors affecting QAOA performance, including different transpilation optimization levels and classical optimizer selection. Our results demonstrate that optimization level 3 reduced circuit depth by 32% compared to level 0 for p=3 circuits, while maintaining solution quality. Among classical optimizers, COBYLA achieved an 81.24% approximation ratio with only 54.8 function evaluations at p=2, outperforming both grid search and SPSA methods. Execution on IBM’s real quantum hardware resulted in performance degradation ranging from 16% at p=1 to 34% at p=3 compared to ideal simulations, highlighting the compounding impact of noise and gate errors as circuit depth increases.These findings provide practical guidance for quantum algorithm implementation on NISQ devices, demonstrating that appropriate selection of transpilation techniques and optimization methods can substantially improve quantum resource efficiency while maintaining solution quality.
The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.
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.
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 promises to solve complex problems beyond the capabilities of classical computers. However, the practical implementation of quantum algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices is significantly challenged by various noise sources that degrade computational fidelity. Transpilation—the process of converting high-level quantum circuits into optimized, hardware-specific instructions—plays a crucial role in mitigating these noise effects. In this paper, we present a comprehensive study on enhancing noise resilience in quantum algorithms through advanced transpilation techniques, evaluated using the SupermarQ benchmarking suite. By systematically analyzing the impact of different optimization levels in Qiskit’s transpiler on a diverse set of quantum algorithms, we demonstrate how specific transpilation strategies influence key performance metrics related to noise resilience. Our results show that higher optimization levels can improve metrics such as Liveness (LV) and Parallelism (PL), leading to more reliable quantum computations on NISQ hardware. This work contributes to the development of noise-adaptive transpilation methods that incorporate noise characteristics into the optimization process, ultimately enhancing the practical viability of quantum algorithms.
Quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve NP-hard problems in near-term gate-based noisy quantum devices. In QAOA, the gate parameters of a parameterized quantum circuit (PQC) are varied by a classical optimizer to generate a quantum state with a significant support to the optimal solution. The existing analysis fails to consider nonidealities in the qubit quality i.e., short lifetime and imperfect gate operations in a realistic quantum hardware. In this article, we study the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analysis indicates that QAOA performance is noise-sensitive (especially higher-depth QAOA instances). Therefore, the optimal number of stages (p-value) for any QAOA instance is limited by the noise in the target hardware as opposed to the current perception that QAOA will provide monotonically better performance with higher-depth. We show that the two-qubit gate error has to be decreased by more than 75% of the current state-of-the-art levels to attain a performance within 10% of the maximum value for the lowest-depth QAOA.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for near-term quantum advantage in combinatorial optimization. A central design parameter is circuit depth p, with theoretical analyses suggesting higher p monotonically improves solution quality. This paper presents empirical evidence that this theoretical relationship does not hold on current noisy intermediate-scale quantum (NISQ) hardware for fault tree analysis applications. Across 120 QAOA executions on 60 QUBO-encoded fault tree instances (N ∈ {12, 16, 20, 24, 28, 32}) on IBM quantum hardware, circuit depths p = 1 and p = 2 were directly compared. The mean change in optimal state sampling probability from doubling circuit depth was Δmax_prob = 1.22 × 10⁻⁵ with a median Δ of zero, making the difference statistically indistinguishable from noise across all evaluated metrics. Output distribution entropy approaches the theoretical maximum (mean = 12.74 bits), indicating hardware noise dominates algorithmic signal. These findings establish that for fault tree minimal cut set identification on current NISQ devices, computational resources are more effectively allocated to increased shot counts than to circuit depth. Complete experimental artifacts with SHA-256 verification are provided, enabling full reproducibility.