Where NISQ-Era Quantum Optimization Stands Today: An Honest Benchmark of QAOA Against Classical Heuristics on a Real-World Exam-Scheduling Max-Cut Problem
Full-pipeline benchmark of the Quantum Approximate Optimization Algorithm (QAOA) against classical combinatorial solvers on a weighted Max-Cut formulation of exam-scheduling conflict minimization. Compares random assignment, greedy heuristic, 2-opt local search, exact ILP (OR-Tools), and QAOA — first via noisy local simulation on an 18-qubit validation subset, then via live execution on IBM's ibm_marrakesh (Heron r2) processor at the full 42-qubit scale. Uses shot-weighted expected-value scoring throughout rather than best-observed-sample reporting. At 18 qubits QAOA reaches 95.4% of the proven optimum; at 42 qubits the hardware run's expected value falls below random guessing (49.05% vs 50.00%), with all 4,096 shots returning distinct bitstrings — the signature of decoherence overwhelming the circuit. Includes causal analysis of the failure mode and outlines planned comparison against quantum annealing hardware.
Full-pipeline benchmark of the Quantum Approximate Optimization Algorithm (QAOA) against classical combinatorial solvers on a weighted Max-Cut formulation of exam-scheduling conflict minimization. Compares random assignment, greedy heuristic, 2-opt local search, exact ILP (OR-Tools), and QAOA — first via noisy local simulation on an 18-qubit validation subset, then via live execution on IBM's ibm_marrakesh (Heron r2) processor at the full 42-qubit scale. Uses shot-weighted expected-value scoring throughout rather than best-observed-sample reporting. At 18 qubits QAOA reaches 95.4% of the proven optimum; at 42 qubits the hardware run's expected value falls below random guessing (49.05% vs 50.00%), with all 4,096 shots returning distinct bitstrings — the signature of decoherence overwhelming the circuit. Includes causal analysis of the failure mode and outlines planned comparison against quantum annealing hardware.
This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.
The transition from theoretical quantum computing to practical real-world applications heavily relies onhybrid quantum-classical architectures designed for NoisyIntermediate-Scale Quantum (NISQ) devices. Among these approaches, the Quantum Approximate Optimization Algorithm(QAOA) is a prominent strategy for addressing complex combinatorial optimization challenges, such as the NP-hard MaxCut problem. Instead of performing the entire computationon a quantum processor, QAOA utilizes a quantum circuit toevaluate a parameterized cost function, whereas a classical optimizer refines the parameters iteratively. This study presentsa rigorous empirical evaluation comparing the performanceof QAOA against established classical solvers on small-scaleMax-Cut instances. All experiments were implemented andexecuted using Python (Qiskit Aer) on a state-vector simulator.Using Erdős–Rényi random graphs and regular graphs with4 to 20 nodes, we benchmark QAOA at depths p = 2 andp = 3 against simulated annealing, the Goemans–WilliamsonSDP-based algorithm, and a linear-time greedy heuristic. Ourexperimental results demonstrate that low-depth QAOA implementations exhibit severe performance degradation, prohibitive computational overhead (O(2^n) scaling), and low convergencerates compared to mature classical algorithms. At 20 nodes,QAOA (p = 2) achieves only a 0.467 approximation ratio versus0.856 for Goemans–Williamson, with a 210× runtime slowdownover greedy heuristics
This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.
The Quantum Approximate Optimization Approach (QAOA) is a hybrid quantum-classical approach designed for solving NP-hard combinatorial optimization problems on Noisy Intermediate-Scale Quantum (NISQ) devices. This study applies QAOA on a four-node Max-Cut problem to investigate the output between two IBM Quantum backends: ibm_torino (Heron r1) and ibm_brisbane (Eagle r3). The experiment uses fixed variational parameters γ=1.2 and β=2.4 for both backends, with a circuit depth of p=2. The ibm_torino backend always produced the right Max-Cut solutions by giving the right optimal bitstrings (0101 and 1010). The ibm_brisbane backend, on the other hand, sometimes gave the wrong bitstrings more often than the right ones. A hypothesis-driven analysis ascribes this discrepancy to variations in backend architecture, qubit connectivity, and parameter sensitivity, in addition to the simplicity of the unweighted four-node network employed.
This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.
The Quantum Approximate Optimisation Algorithm (QAOA) has emerged as a leading candidate for near-term quantum advantage in combinatorial optimisation, but most evaluations remain confined to synthetic benchmarks such as random MaxCut instances. Translating QAOA to real-world problem instances -- with irregular graph structures, heterogeneous constraint types, and practical scale requirements -- introduces additional challenges including QUBO formulation overhead, hardware embedding costs, and the performance gap between QAOA on structured real instances vs. random benchmarks. This paper presents the Real-World QAOA (RW-QAOA) framework, a systematic methodology for applying QAOA to four real-world application domains: supply chain network optimisation, financial portfolio rebalancing, telecommunications frequency assignment, and traffic signal timing optimisation. RW-QAOA introduces three methodological contributions: a domain-adaptive QUBO formulator (DAQF) encoding real-world constraints as penalised QUBO terms with penalty coefficient auto-tuning; a warm-start initialisation strategy (WSIS) using classical heuristic solutions to seed QAOA parameter search; and a layered noise adaptation protocol (LNAP) adjusting circuit depth based on real-time device calibration data. RW-QAOA is evaluated on real problem instances from industry partners across all four domains on IBM Quantum Eagle (127-qubit). RW-QAOA achieves solution quality within 4.2% of classical exact solvers across all four domains, outperforming classical greedy heuristics by 12.4% (SD = 3.8%) on average. WSIS reduces QAOA parameter convergence iterations by 48.4%. LNAP improves approximation ratio by 8.4pp vs. fixed-depth QAOA under device noise variation.