Deploying quantum neural networks (QNNs) on sparse hardware requires preserving task accuracy while reducing compiler-induced two-qubit gates, SWAPs, and depth. We present ConQUESTA (\underline{C}onstrained \underline{Qu}antum \underline{E}ntangler \underline{S}election with \underline{T}opology \underline{A}wareness), a post training pruning framework that combines task saliency with compiler cost, screens candidate entanglers, and searches complete pruning masks under an explicit accuracy constraint. Unlike one-shot ranking, each mask is transpiled as a whole across multiple coupling topologies. Across 4-, 6-, and 8-qubit QNNs and eight model seeds at 55% pruning, ConQUESTA achieves mean resource reductions of 61.6% on Breast Cancer, 72.0% on Digits01, and 82.2% on Iris, exceeding the strongest matched simple baseline by 3.5, 1.7, and 8.9 percentage points, respectively. Fixed-mask recovery raises feasibility from 16/24 to 22/24 runs. In a fixed-k=4 scaling study on a scaling probe of 4 to 12-qubits, the raw mask space grew from 495 to 12.1M while the evaluated masks increase only from 189 to 305. Resource-weight changes alter depth/routing priorities with at most a 0.44-point mean validation shift.
Deploying quantum neural networks (QNNs) on sparse hardware requires preserving task accuracy while reducing compiler-induced two-qubit gates, SWAPs, and depth. We present ConQUESTA (\underline{C}onstrained \underline{Qu}antum \underline{E}ntangler \underline{S}election with \underline{T}opology \underline{A}wareness), a post training pruning framework that combines task saliency with compiler cost, screens candidate entanglers, and searches complete pruning masks under an explicit accuracy constraint. Unlike one-shot ranking, each mask is transpiled as a whole across multiple coupling topologies. Across 4-, 6-, and 8-qubit QNNs and eight model seeds at 55% pruning, ConQUESTA achieves mean resource reductions of 61.6% on Breast Cancer, 72.0% on Digits01, and 82.2% on Iris, exceeding the strongest matched simple baseline by 3.5, 1.7, and 8.9 percentage points, respectively. Fixed-mask recovery raises feasibility from 16/24 to 22/24 runs. In a fixed-k=4 scaling study on a scaling probe of 4 to 12-qubits, the raw mask space grew from 495 to 12.1M while the evaluated masks increase only from 189 to 305. Resource-weight changes alter depth/routing priorities with at most a 0.44-point mean validation shift.
Designing quantum neural networks (QNNs) that are both accurate and deployable on NISQ hardware is challenging. Handcrafted ansatze must balance expressivity, trainability, and resource use, while limited qubits often necessitate circuit cutting. Existing quantum architecture search methods primarily optimize accuracy while only heuristically controlling quantum and mostly ignore the exponential overhead of circuit cutting. We introduce QNAS, a neural architecture search framework that unifies hardware aware evaluation, multi objective optimization, and cutting overhead awareness for hybrid quantum classical neural networks (HQNNs). QNAS trains a shared parameter SuperCircuit and uses NSGA-II to optimize three objectives jointly: (i) validation error, (ii) a runtime cost proxy measuring wall clock evaluation time, and (iii) the estimated number of subcircuits under a target qubit budget. QNAS evaluates candidate HQNNs under a few epochs of training and discovers clear Pareto fronts that reveal tradeoffs between accuracy, efficiency, and cutting overhead. Across MNIST, Fashion-MNIST, and Iris benchmarks, we observe that embedding type and CNOT mode selection significantly impact both accuracy and efficiency, with angle-y embedding and sparse entangling patterns outperforming other configurations on image datasets, and amplitude embedding excelling on tabular data (Iris). On MNIST, the best architecture achieves 97.16% test accuracy with a compact 8 qubit, 2 layer circuit; on the more challenging Fashion-MNIST, 87.38% with a 5 qubit, 2 layer circuit; and on Iris, 100% validation accuracy with a 4 qubit, 2 layer circuit. QNAS surfaces these design insights automatically during search, guiding practitioners toward architectures that balance accuracy, resource efficiency, and practical deployability on current hardware.
Abstract Equivariant quantum neural networks are designed to preserve symmetries in quantum machine-learning data, but this property is usually verified only before hardware compilation. We show that a transpiler can preserve the expected unitary symmetry relation while compiling symmetry-related inputs into circuits with different two-qubit gate counts and physical-qubit layouts, so ideal-circuit equivariance does not guarantee symmetry at the level of compiled circuit structure. We formalise this gap with a three-level compliance hierarchy and a taxonomy separating topology-input ansätze, where the symmetry changes the gate topology the compiler sees, from parameter-input ansätze, where it changes only numerical gate parameters and provably leaves controlled- Z counts unchanged under topology-based transpilation. Auditing four published ansatz families, we observe the effect only in the topology-input case. For the Skolik permutation-equivariant weighted-graph ansatz compiled to the IBM Heron Fez simulator target at twelve qubits, sparse graph inputs produce a mean relative controlled- Z asymmetry of 7.3% across fifty random vertex permutations, with a worst case of 22.5%. The effect persists across all four Qiskit optimisation levels and is not removed by matched-layout compilation, implicating routing-stage sensitivity to the ordered sparse-edge gate sequence. A density sweep shows that the asymmetry is comparable across intermediate graph densities and vanishes for complete graphs, where the ansatz degenerates into the parameter-input class, and stochastic baselines attribute the realised differences to heuristic routing sensitivity rather than to differing optimal compiled costs. Finally, we propose compile-once-and-relabel, a deployment pattern that removes controlled- Z count asymmetry by construction and reduces compilation cost for orbit-based workflows.
One-Shot Structured Pruning of Quantum Neural Networks via q-Group Engineering and Quantum Geometric Metrics
Quantum neural networks (QNNs) suffer from severe gate-level redundancy, which hinders their deployment on noisy intermediate-scale quantum (NISQ) devices. In this work, we propose q-iPrune, a one-shot structured pruning framework grounded in the algebraic structure of q-deformed groups and task-conditioned quantum geometry.
Unlike prior heuristic or gradient-based pruning methods, q-iPrune formulates redundancy directly at the gate level. Each gate is compared within an algebraically consistent subgroup using a task-conditioned q-overlap distance, which measures functional similarity through state overlaps on a task-relevant ensemble. A gate is removed only when its replacement by a subgroup representative provably induces a bounded deviation on all task observables.
We establish three rigorous theoretical guarantees. First, we prove completeness of redundancy pruning: no gate that violates the prescribed similarity threshold is removed. Second, we show that the pruned circuit is functionally equivalent up to an explicit, task-conditioned error bound, with a closed-form dependence on the redundancy tolerance and the number of replaced gates. Third, we prove that the pruning procedure is computationally feasible, requiring only polynomial-time comparisons and avoiding exponential enumeration over the Hilbert space.
To adapt pruning decisions to hardware imperfections, we introduce a noise-calibrated deformation parameter λ that modulates the q-geometry and redundancy tolerance. Experiments on standard quantum machine learning benchmarks demonstrate that q-iPrune achieves substantial gate reduction while maintaining bounded task performance degradation, consistent with our theoretical guarantees.
Variational quantum circuits (VQCs) suffer from barren plateaus, where gradients vanish exponentially with system size, limiting effective optimization. While prior mitigation strategies focus on circuit design and initialization, the effect of circuit compression – specifically, which gates are removed – on trainability remains comparatively unexplored. In this work we study quantum gate pruning from a trainability perspective in a controlled, noiseless 6-qubit simulation testbed, and report numerical evidence that gate-selection criterion plays a substantial role in preserving the optimization landscape of compressed circuits. We propose Q-AGASP, a saliency-based pruning framework that ranks parameterized quantum gates using a combination of gradient-weight sensitivity and quantum activation, and introduce a Quantum Fisher Information (QFI)-motivated saliency variant that targets parameters associated with low gradient variance. Both approaches are applied through an iterative pruning schedule with frozen weights. Experiments on a hybrid quantum-classical model (6-qubit, 144-parameter VQC) show that saliency-guided pruning improves the gradient variance of the surviving parameters relative to uninformed methods – by 6–9 $\times $ at 90% gate sparsity in our tested regime – while random or magnitude-based pruning can produce near-zero gradient variance in some seeds. We further find that post-fine-tuning accuracy converges across methods under our 15-epoch fine-tuning budget, which suggests that accuracy and pre-fine-tuning gradient variance are complementary rather than interchangeable diagnostics, with accuracy becoming less discriminative precisely when the fine-tuning budget is generous relative to circuit size. To analyze how gate rankings evolve during compression we introduce saliency drift, a Spearman-rank-correlation-based metric, and derive a distribution-free bound relating the observed correlation to the magnitude of ranking reshuffles; drift increases with sparsity in our experiments, consistent with iterative recomputation capturing structural changes not visible to one-shot pruning. We are explicit that these findings are numerical observations from a single ansatz, qubit count, and dataset rather than architecture-independent theorems, and we discuss how ansatz topology, entanglement structure, and circuit depth would be expected to modulate them, together with the changes needed to extend the framework to noisy hardware and to chemistry-motivated ansätze.
Training quantum neural networks (QNNs) on quantum hardware is currently bottlenecked by the cost of gradient estimation: standard parameter-shift methods require a number of circuit evaluations that grows quadratically with the number of trainable parameters, making hardware-based optimisation impractical beyond small system sizes. In this work, we introduce a training framework that reduces this cost to logarithmic in the number of qubits, making gradient-based QNN optimisation feasible on near-term hardware at increasing scales.
Our framework combines three co-designed ingredients: (i) a structured, subspace-preserving Butterfly circuit architecture with O(nlogn) parameters and logarithmic depth; (ii) a layer-wise training strategy that confines on-hardware optimisation to one small, well-structured layer at a time; and (iii) a parallelised parameter-shift rule that exploits the commuting structure within each Butterfly layer to extract all gradients in a constant number of circuit executions. Together these reduce the number of distinct circuit evaluations per optimisation step from O(n2) to O(logn).
We validate the framework on clinical data imputation using the MIMIC-III electronic health record dataset, a demanding benchmark sensitive to optimisation instability and model variance. Hybrid classical-quantum models are trained directly on IonQ Forte Enterprise trapped-ion hardware at 16 qubits without performance degradation relative to ideal or noisy simulation and via tensor-network simulation at 32 qubits, with 32-qubit inference executed on hardware. The resulting models match or exceed strong classical neural baselines in downstream patient survival prediction while exhibiting reduced variance across runs, demonstrating that the proposed framework enables practical, scalable QNN training under realistic hardware constraints.
Quantum machine learning (QML) promises new representational and computational capabilities, yet practical deployment on near-term hardware is hampered by resource overheads, depth constraints, and fragile trainability. This thesis advances resource-aware QML by proposing architectures and kernels that retain expressivity while sharply reducing qubit counts, circuit depth, and entangling-gate budgets. The work is presented in an article-based format with three core contributions. First, I introduce a Coherent Feed-Forward Quantum Neural Network (CFF-QNN) that preserves quantum coherence across all layers, mirrors the flexibility of classical feed-forward networks (adjustable hidden layers and nodes), and decouples qubit requirements from input feature dimension. Compared to prevailing QNN baselines, the CFF-QNN reduces both depth and CNOT count by over 50% while achieving strong performance on standard benchmarks (e.g., 91% accuracy on Wisconsin breast cancer and 85% on credit-card fraud). This contribution is accompanied by an international patent filing (WO2025050205A1). Second, I develop a resource-efficient quantum kernel that enables high-dimensional embeddings with substantially fewer qubits and entanglers, achieving linear scaling of entangling gates in the number of qubits. Empirically, the kernel delivers competitive or superior performance to widely used classical kernels and to popular quantum feature maps (e.g., on the Parkinson's disease dataset), with noisy simulations and small-scale runs on superconducting hardware indicating suitability for near-term devices. This contribution is covered by a companion patent filing (WO2025073041A1). Third, I propose a quantum reservoir computing (QRC) scheme that reuses a fixed quantum feature-map circuit as the reservoir while injecting temporal memory via an explicit feedback loop. The register is recycled across time, so quantum resources remain constant, no quantum parameters are trained, and only a lightweight classical readout is fitted. Experiments on chaotic time series (e.g., Mackey-Glass) show competitive predictive accuracy with strict resource efficiency, and illuminate how feedback delay and entangling structure affect memory and error. Collectively, these results chart a path toward practical QML: coherent architectures and kernels that are trainable, scalable in input dimension, frugal in quantum resources, and viable on noisy intermediate-scale devices—while providing design guidelines for future, larger-scale implementations.
Muhammad Shafique