Abstract Quantum benchmarks for artificial intelligence require measurement budgets, target observables, and execution records to agree. We reanalyze archived signed-overlap, kernel, and quantum approximate optimization algorithm (QAOA) summaries from a cloud-hardware campaign, retaining incomplete runs and distinguishing measured entries from imposed values. For eight signed-overlap submissions, increasing shots per batch from 256 to 2048 changes reconstructed root-mean-square error from 0.1335 to 0.1292. At 2048 shots, squared offsets of the empirical batch means account for 98.2% of the reconstructed error. This decomposition is descriptive; it does not identify a physical noise mechanism. An incomplete kernel contains 18 measured off-diagonal entries out of 45; filling the others with zero changes its observed-entry mean from 0.2220 to 0.0888. A source-label conflict prevents a matched provider comparison. Across 43 Rigetti QAOA submissions, size-group mean edge-cut fractions range from 0.4782 to 0.5010, but heterogeneous parameters and absent raw histograms limit interpretation. Earlier learning and simulation results obtained with graphics processing units provide exploratory supplementary evidence.
Abstract Quantum benchmarks for artificial intelligence require measurement budgets, target observables, and execution records to agree. We reanalyze archived signed-overlap, kernel, and quantum approximate optimization algorithm (QAOA) summaries from a cloud-hardware campaign, retaining incomplete runs and distinguishing measured entries from imposed values. For eight signed-overlap submissions, increasing shots per batch from 256 to 2048 changes reconstructed root-mean-square error from 0.1335 to 0.1292. At 2048 shots, squared offsets of the empirical batch means account for 98.2% of the reconstructed error. This decomposition is descriptive; it does not identify a physical noise mechanism. An incomplete kernel contains 18 measured off-diagonal entries out of 45; filling the others with zero changes its observed-entry mean from 0.2220 to 0.0888. A source-label conflict prevents a matched provider comparison. Across 43 Rigetti QAOA submissions, size-group mean edge-cut fractions range from 0.4782 to 0.5010, but heterogeneous parameters and absent raw histograms limit interpretation. Earlier learning and simulation results obtained with graphics processing units provide exploratory supplementary evidence.
Estimating an N×N quantum kernel from circuit fidelities requires Θ(N2S) measurement shots, the dominant bottleneck for deployment on near-term hardware. Existing budget-saving methods (Nyström-QKE, ShoFaR, kernel-target alignment) sub-sample \emph{which} entries to measure but allocate shots \emph{uniformly} within their chosen subset, ignoring how much each entry drives the downstream classifier. We close this gap with two contributions. \textbf{First, a complete regime decomposition} for shot-budgeted quantum kernel learning: a principled menu of when each allocator wins. Our method, \emph{AQKA}, dominates the budget-limited regime (B≲16npairs) on sparse-sensitivity KRR, with the gap \emph{growing} from +8 to +25 pts over uniform as N scales 225→1000 and reaching +26--32 pts on an \texttt{ibm\_pittsburgh} (156-qubit Heron) hardware kernel; Nyström-QKE wins at saturating budgets on planted-sparse via low-rank reconstruction; ShoFaR is competitive only at extreme low budgets. \textbf{Second, a closed-form pair-level acquisition theory}: sij⋆∝∣gij∣Kij(1−Kij) with explicit gradient gij for KRR (Lemma~1, ∣βiαj+βjαi∣Kij(1−Kij)) and SVM via the envelope theorem (∣ηi∗ηj∗∣Kij(1−Kij)); a \emph{corrected} sparsity-aware Cauchy--Schwarz rate ρ≤2m/N matching empirics (vs.\ the naive m2/N2); an explicit-constant plug-in regret bound (Theorem~2); and a tighter SVM ceiling ρSVM≤msv2/N2. We close with the first multi-seed live online adaptive shot allocation on quantum hardware: +17.0±4.8 pts at N=20 on \texttt{ibm\_aachen} (3.5σ, 5 seeds), with the advantage holding at N=30 at higher budget on \texttt{ibm\_berlin} (+14.0±8.5 pts, 5 seeds).
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.
Abstract We formalize Quantum Hybrid Modules (QHM) to evaluate the insertion of quantum subroutines into classical AI pipelines with explicit assumptions about data loading, noise, and measurement overhead. The framework comprises three components: (1) a Hadamard Quantum Self-Attention (HQSA) module computing sparse attention via Hadamard-test inner products in O(nn/k⋅logd/ϵ) time assuming quantum random access memory (qRAM); (2) a Quantum Approximate Optimization Algorithm (QAOA) module for combinatorial optimization sub-problems; and (3) a Grover-accelerated neurosymbolic verification loop for quadratically faster constraint checking. We evaluate QHM through 22 experiments spanning statevector and GPU simulation up to 30 qubits, cloud simulators, and five quantum processing unit (QPU) experiments on Rigetti Cepheus and IonQ Forte, including 8--100-qubit superconducting and 8--30-qubit trapped-ion QAOA. Simulations confirm the intended mechanisms: QAOA exceeds the Goemans--Williamson bound on selected 3-regular instances, Hadamard-test attention reproduces classical softmax, and Grover verification reaches a 20,862× query reduction at 30 qubits. Classical, dequantized, and qRAM-free baselines expose current limits: small quantum kernels lag tuned classical baselines, hybrid variational quantum circuit layers add training cost without consistent accuracy gains, and shot-based noisy intermediate-scale quantum (NISQ) attention is limited by systematic bias. Hardware results are depth- and platform-dependent: shallow circuits retain measurable signal, Rigetti QAOA depolarizes to the random baseline and is not recovered by post-hoc mitigation, and IonQ Forte preserves QAOA signal but remains below noiseless performance. We do not claim near-term quantum advantage; we characterize the gap between asymptotic theory and present-day hardware.
Training parameterized quantum circuits requires balancing optimization progress with limited evaluation budgets and the statistical uncertainty of near-term quantum hardware. We present a modular benchmarking framework that separates quantum search-direction estimation from classical parameter-update rules, allowing their interactions and sensitivities to be examined independently. We evaluate a suite of gradient-based, stochastic, and derivative-free optimizers across combinatorial optimization using the Quantum Approximate Optimization Algorithm (QAOA), supervised quantum machine learning using Iris classification and a quantum convolutional neural network (QCNN) for binary MNIST classification, and quantum chemistry using the variational quantum eigensolver (VQE) for molecular hydrogen. By separating objective evaluations from sample-circuit costs under finite-shot simulation and physical execution on a 156-qubit processor, we compare optimizer behavior across workloads with different parameter counts and measurement requirements. Four selected simulator and hardware case studies report terminal and best observed objectives separately, alongside post-training classifier accuracies. The comparisons include selected MaxCut and hydrogen trajectories and illustrate workload-dependent objective changes and evaluation costs, while the simulator benchmark compares both peak and mean performance across three seeds. The hardware runs do not establish an optimizer ranking or isolate a causal effect of device noise.
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.
On a cloud-accessed quantum processor the classical optimizer of a variational algorithm communicates with the device through submitted jobs, and each job carries a queueing and turnaround overhead that does not depend on how many circuits it contains. We study a simple consequence of this for the quantum approximate optimization algorithm (QAOA). An optimizer whose next set of trial parameters is known before any result returns can evaluate the whole set in one job, whereas a sequential optimizer such as COBYLA spends one job per function evaluation. We compare a batched pattern search with COBYLA on IBM's \ibmfez\ processor for cardinality-constrained portfolio selection with six to twelve assets, giving both optimizers the same number of jobs and the same number of shots. At every size the batched search reaches, after its first job, a parameter quality that the serial optimizer takes several jobs to match, and the two methods converge to comparable final values; repeating the eight-asset comparison from four starting points gives the same ordering each time. The instances are small enough to be solved exactly, which lets us check that the device's output distribution is correlated with the true ranking of portfolios and is clearly separated from a control circuit of the same depth with the cost layer removed. A short scan over circuit depth at classically optimal parameters shows that on this device the measured solution quality peaks at two or three QAOA layers. The protocol is described in enough detail to be reproduced, and the notebooks and raw counts are released.