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.
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.
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.
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 establishing asymptotic convergence under idealized conditions. This paper presents a limits study demonstrating that this theoretical relationship does not translate to measurable improvement 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 (ibm_torino, 133-qubit Heron processor), 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. For 8,192 shots, the binomial sampling uncertainty is O(10⁻²); the observed mean delta is therefore approximately three orders of magnitude below the shot-noise scale, making the difference statistically indistinguishable from zero. Output distribution entropy approaches the theoretical maximum of log₂(8192) ≈ 13 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.
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.
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.
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 Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently know about the capabilities of QAOA, or of the difficulty of the requisite parameters optimization. Here, we study the performance of QAOA on the MaxCut combinatorial optimization problem, optimizing the quantum circuits on a classical computer using automatic differentiation and stochastic gradient descent, using QuantumFlow, a quantum circuit simulator implemented with TensorFlow. We find that we can amortize the training cost by optimizing on batches of problems instances; that QAOA can exceed the performance of the classical polynomial time Goemans-Williamson algorithm with modest circuit depth, and that performance with fixed circuit depth is insensitive to problem size. Moreover, MaxCut QAOA can be efficiently implemented on a gate-based quantum computer with limited qubit connectivity, using a qubit swap network. These observations support the prospects that QAOA will be an effective method for solving interesting problems on near-term quantum computers.