Factorial Benchmarking of Exact and Finite-Shot Gradient Resolvability in a Four-Qubit Hybrid Quantum Neural Network
Abstract
Abstract Gradient resolvability in quantum neural networks can depend simultaneously on circuit structure, objective construction, and finite-shot measurement, yet these interventions are usually benchmarked separately. We use a complete 2³ factorial design to test interactions among a pair-restricted controlled-NOT (CNOT) schedule (E), normalized transverse-field Ising model (TFIM) energy objective (L), and fixed residual shortcut (R) in a four-qubit measure–re-encode–reset hybrid quantum neural network. Across 50 matched initialization clusters and 30 finite-shot replicates per scientific cell, configurations were matched by block count, parameter identity, and total implemented simulator-shot budget. The centered E × L interaction in exact-gradient magnitude was positive and was supported by both mixed-model inference and an initialization-cluster bootstrap; the positive direction was retained in an independent-seed dataset, although its magnitude and depth profile remained uncertain. Finite-shot E × L and E × R interactions met the protocol-derived Wald/Holm rule, but their 1,000-fit nested-bootstrap intervals included zero, and the residual result was estimator-mode sensitive and inactive at D = 1, 2. The L × R-by-depth interaction remained unresolved. These results show that factorial benchmarking can expose composition effects that marginal comparisons miss while separating exact-gradient signal from finite-shot estimator behavior. They do not establish optimization…
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