Overview As quantum processors scale into the utility regime (≥ 100 qubits), evaluating hardware fidelity on algorithmically relevant workloads becomes severely constrained. Prevailing methodologies such as Randomized Benchmarking (RB) characterize synthetic Clifford averages, while Cross-Entropy Benchmarking (XEB) is fundamentally bottlenecked by the exponential classical simulation cost of calculating statevectors beyond 50 qubits. In this work, we introduce AlgoInvar, an in situ, simulation-free, parameter-free benchmarking framework that provides an algorithm-specific complementary diagnostic layer by anchoring hardware evaluation to exact algebraic conservation laws and continuous physical symmetries in Variational Quantum Eigensolver (VQE) fermionic chemistry and Quantum Approximate Optimization Algorithm (QAOA) combinatorial optimization circuits. Core Mathematical Invariants Fermionic VQE Particle-Number Conservation QAOA Global Z2\mathbb{Z}_2Z2 Spin Parity Invariance Empirical Validation on 156-Qubit IBM Heron r2 Processors We demonstrate an initial physical proof-of-principle deployment on connected sub-chains of two independent 156-qubit IBM Heron r2 utility-era processors (ibm_kingston and ibm_fez): Execution Efficiency: Single-job batched executions with 8,192 shots per circuit (40,960 total physical shots per system) executed in exactly 13.0 seconds of QPU runtime. In-Sector Retention & Leakage Directional Asymmetry Diagnostic Classical Computational Scaling Controlled Simulation Suite & Active Error Mitigation 4-Channel Parameterized Noise Sweeps: Evaluated under Kraus operator models for longitudinal thermal relaxation (T1), pure phase dephasing (T2∗), coherent angle over-rotations, and asymmetric readout confusion. Active Molecular H2\mathrm{H}_2H2 VQE Symmetry Mitigation: Post-selection onto the physical 𝑤 = 2 sector suppresses runaway dissipation under composite noise, reducing energy error from 520.6 mHa down to 369.6 mHa (a 29.0% reduction). Open Science & Code Repository GitHub Repository: https://github.com/Quantum-Computing-Researcher/AlgoInvar Author: Rehan Arqam (rarqam14@gmail.com) Affiliation: Independent Researcher, Islamabad, 44000, Pakistan.
Overview As quantum processors scale into the utility regime (≥ 100 qubits), evaluating hardware fidelity on algorithmically relevant workloads becomes severely constrained. Prevailing methodologies such as Randomized Benchmarking (RB) characterize synthetic Clifford averages, while Cross-Entropy Benchmarking (XEB) is fundamentally bottlenecked by the exponential classical simulation cost of calculating statevectors beyond 50 qubits. In this work, we introduce AlgoInvar, an in situ, simulation-free, parameter-free benchmarking framework that provides an algorithm-specific complementary diagnostic layer by anchoring hardware evaluation to exact algebraic conservation laws and continuous physical symmetries in Variational Quantum Eigensolver (VQE) fermionic chemistry and Quantum Approximate Optimization Algorithm (QAOA) combinatorial optimization circuits. Core Mathematical Invariants Fermionic VQE Particle-Number Conservation QAOA Global Z2\mathbb{Z}_2Z2 Spin Parity Invariance Empirical Validation on 156-Qubit IBM Heron r2 Processors We demonstrate an initial physical proof-of-principle deployment on connected sub-chains of two independent 156-qubit IBM Heron r2 utility-era processors (ibm_kingston and ibm_fez): Execution Efficiency: Single-job batched executions with 8,192 shots per circuit (40,960 total physical shots per system) executed in exactly 13.0 seconds of QPU runtime. In-Sector Retention & Leakage Directional Asymmetry Diagnostic Classical Computational Scaling Controlled Simulation Suite & Active Error Mitigation 4-Channel Parameterized Noise Sweeps: Evaluated under Kraus operator models for longitudinal thermal relaxation (T1), pure phase dephasing (T2∗), coherent angle over-rotations, and asymmetric readout confusion. Active Molecular H2\mathrm{H}_2H2 VQE Symmetry Mitigation: Post-selection onto the physical 𝑤 = 2 sector suppresses runaway dissipation under composite noise, reducing energy error from 520.6 mHa down to 369.6 mHa (a 29.0% reduction). Open Science & Code Repository GitHub Repository: https://github.com/Quantum-Computing-Researcher/AlgoInvar Author: Rehan Arqam (rarqam14@gmail.com) Affiliation: Independent Researcher, Islamabad, 44000, Pakistan.
Despite rapid progress in quantum optimization, broad real-hardware benchmarks comparing multiple algorithmic families across diverse combinatorial problems under a common protocol remain limited. We benchmark gate-based quantum optimization on four NP-hard problems: multi-dimensional knapsack (MDKP), maximum independent set (MIS), quadratic assignment (QAP), and market-share (MSP). We study VQE, CVaR-VQE, standard, multi-angle, and warm-start QAOA, together with qubit-efficient PCE and QRAO, on IBM Heron r1/r2 processors using resilience-level-2 mitigation. To our knowledge, this includes the first real-hardware QRAO results and the first multi-problem PCE hardware benchmark.
Across 247 method-instance combinations, we report transpiled circuit size, hardware outcomes, and an independent-error gate-count fidelity proxy, Fest. For MDKP and MIS, an empirical operating point near Fest≈0.1, corresponding to about 770 two-qubit gates at the median Heron-r2 CZ error rate, marks the onset of noise-dominated execution. QAP exposes a separate bottleneck: dense one-hot encodings and an exponentially sparse feasible manifold, with feasible fraction 10!/2100 at n=10; no tested hardware method produces a feasible assignment. Compiled QAOA-family circuits are generally noise dominated, and a matched uniform-random control shows that most feasible low-fidelity outcomes fall within the random range, apart from one finite-sample MIS warm-start exception. A SWAP-aware, fractional-gate, Nighthawk-topology compilation counterfactual reduces two-qubit counts but leaves all circuits below Fest=10−3. These conclusions apply to the tested implementations rather than QAOA in general. Qubit-efficient methods extend runnable instance sizes, but only within the empirical fidelity budget.
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.
Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.
Quantum processors have crossed the one-hundred-qubit mark, but noise continues to limit circuit performance, while full quantum error correction remains too costly for routine use. Error suppression and mitigation therefore play an important role in extracting value from current hardware, yet independent comparisons of commercial solutions on identical workloads and devices remain scarce. We benchmark IBM Qiskit Runtime, Q-CTRL Performance Management, and Qedma QESEM on IBM Pittsburgh, a 156-qubit IBM Quantum Heron r3 processor. For Sampler workloads, we run Bernstein-Vazirani, quantum phase estimation, GHZ-state preparation, and randomized mirror circuits with up to 100 measured qubits, comparing raw execution, IBM measurement twirling, and Q-CTRL. For Estimator workloads, we measure chain-averaged magnetization and correlation observables of an eight-layer transverse-field Ising circuit at 25, 50, and 75 qubits against an exact matrix-product-state reference, comparing IBM raw execution, IBM TREX plus twirling, Q-CTRL, and QESEM. Q-CTRL produced the best results on the three structured Sampler workloads while keeping reported QPU times within the same order as the IBM configurations. Across six Ising observable and system-size cases, aggregate mean absolute error was 0.0883 for IBM raw execution, 0.0807 for IBM TREX plus twirling, 0.0285 for Q-CTRL, and 0.0188 for QESEM. Relative to raw execution, Q-CTRL and QESEM reduced aggregate error by factors of 3.10 and 4.70, respectively, while QESEM used 7.5 to 11.1 times the reported QPU time of Q-CTRL. These results show that managed error suppression and mitigation can substantially improve current hardware performance, but with distinct accuracy and execution-time tradeoffs.
Abstract Quantum computers promise to solve electronic structure, lattice dynamics, and strongly correlated problems beyond classical reach. However, near-term noisy intermediate scale quantum (NISQ) processors require systematic benchmarking to establish where variational algorithms with error mitigation can achieve chemical accuracy and cor rectly predict physical phenomena. Here we present 28 quantum material simula tions implemented with Qiskit, spanning molecular hydrogen (H 2 ) through the iron molybdenum cofactor (FeMoco), one-dimensional Hubbard chains, Kitaev honeycomb spin liquids, topological insulators (SSH model), BCS superconductors, and disordered Anderson insulators. Using the variational quantum eigensolver (VQE) with UCCSD ansatz, we achieve chemical accuracy (±1.6 mHa) for H 2 across the full dissociation curve and recover exact ground-state energies for H4 within 9 mHa after zero-noise extrapolation (ZNE) — reducing raw VQE errors from 152 mHa to 9 mHa. We accu rately identify the transverse-field Ising quantum critical point (h c = J) with 4 qubits, resolve Majorana Dirac dispersions in the Kitaev spin liquid, and reproduce the Mott transition in the Fermi-Hubbard model at U c = 6t. Resource estimation for FeMoco reveals O(N 2.5 ) scaling, projecting chemical accuracy with ∼200 logical qubits. Across all benchmarks, we quantify the accuracy-circuit depth tradeoff, demonstrating that depth-6 VQE ans¨atze achieve chemical accuracy for small molecules while depth-10 is required for correlated lattices. These results establish a comprehensive benchmark suite for evaluating quantum hardware, error mitigation protocols, and variational al gorithms for materials science on NISQ processors.
This paper presents an empirical evaluation of the Qube Engine, a hybrid quantum-classical Variational Quantum Regressor (VQR) implemented on Noisy Intermediate-Scale Quantum (NISQ) systems. The framework integrates classical data encoding via single-qubit rotations, parameterized RY+RZ variational layers, and linear entangling circuits evaluated on 4-qubit quantum registers. Optimization is conducted using classical algorithms (COBYLA) targeting Pauli-Z expectation values and Mean Squared Error (MSE) loss on continuous feature spaces. We evaluate model performance across ideal statevector simulation (AerSimulator) and physical IBM Quantum superconducting processors (ibm_marrakesh, ibm_fez, ibm_kingston). Experimental results demonstrate consistent optimization dynamics and low simulation-to-hardware expectation drift (Δ=0.0188), corresponding to a 98.23% cross-backend output stability score under shallow circuit depths. This work provides a realistic analysis of variational regression dynamics, hardware execution variance, and structural trade-offs for near-term quantum machine learning models on NISQ hardware.