Sparse Modulated Quantum Neural Networks (SMQNN): Architectural Mitigation of Barren Plateaus via Modular Entanglement and Physical Hardware Validation

Variational Quantum Algorithms (VQAs) face two compounding obstacles on Noisy Intermediate-Scale Quantum (NISQ) hardware: the barren plateau phenomenon, wherein gradient variancevanishes exponentially with system size n, and device decoherence, which degrades coherent signalbefore classical optimizers can act. We introduce the Sparse Modulated Quantum Neural Network(SMQNN), a hardware-native ansatz that resolves both obstacles through a single structural principle:replacing global entanglement with block-diagonal modules of fixed width k, interconnected exclusivelyby classical Mid-Circuit Measurements (MCMs). We prove that the gradient variance of SMQNN islower-bounded by Ω(∥Wm∥22· 4−k), independent of total system size n, thereby providing a provableescape from exponential trainability collapse. We further prove that classical state preparation atmodule boundaries resets depolarization entropy, reducing the effective error-accumulation lengthfrom k to keff = k(1 − fmcm/2). This yields an exponential improvement in the signal-to-noiseratio parameterized by the reset fraction fmcm, with similar principles applying to trapped-ion andneutral-atom error models as validated by simulation. We validate SMQNN empirically on a physical156-qubit IBM Marrakesh Heron-architecture processor using 4096 shots per experiment and TwirledReadout Error Extinction. Across three physically distinct benchmarks—topological phase transitionsin the Su-Schrieffer-Heeger (SSH) model, Many-Body Localization (MBL) imbalance dynamics,and Quantum Error Correction (QEC) syndrome detection—SMQNN consistently outperformsdepth-matched dense-VQC baselines. Edge parity accuracy improved from 0.83 (dense) to 0.90(SMQNN); syndrome correction fidelity improved from 45% to 80%. We explicitly characterizethe expressivity trade-off: SMQNN achieves a 28× reduction in ground-state accuracy for globallyentangled Hamiltonians, confirming its intended domain as topological, localized, or modular quantumphenomena. We systematically characterize the expressivity-noise trade-off, demonstrating thatSMQNN intentionally restricts Hilbert space to provide robust scaling specifically for spatiallylocal problems. Finally, we demonstrate platform-agnostic generality via simulations of trapped-ionand neutral-atom noise regimes, expanding the SMQNN architecture into a comprehensive toolkitfor NISQ algorithm design. All circuits, gate counts, and IBM Job IDs are open-sourced for fullreproducibility.