Quantum Neural Networks

We propose a quantum implicit neural representation (QINR)-based autoencoder (AE) and variational autoencoder (VAE) for image reconstruction and generation tasks. Our purpose is to demonstrate that the QINR in VAEs and AEs can transform information from the latent space into highly rich, periodic, and high-frequency features. Additionally, we aim to show that the QINR-VAE can be more stable than various quantum generative adversarial network (QGAN) models in image generation because it can address the low diversity problem. Our quantum-classical hybrid models consist of a classical convolutional neural network (CNN) encoder and a quantum-based QINR decoder. We train the QINR-AE/VAE with binary cross-entropy with logits (BCEWithLogits) as the reconstruction loss. For the QINR-VAE, we additionally employ Kullback-Leibler divergence for latent regularization with beta/capacity scheduling to prevent posterior collapse. We introduce learnable angle-scaling in data reuploading to address optimization challenges. We test our models on the MNIST, E-MNIST, and Fashion MNIST datasets to reconstruct and generate images. Our results demonstrate that the QINR structure in VAE can produce a wider variety of images with a small amount of data than various generative models that have been studied. We observe that the generated/reconstructed images from the QINR-VAE/AE are clear with sharp boundaries and details. Overall, we find that the addition of QINR-based quantum layers into the AE/VAE frameworks shows improved performance of reconstruction/generation under the constrained experimental setting relative to the specific baselines.

Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning capability. We study this question in the pure-state setting by viewing encoded data as an embedded manifold in $\mathbb{C}P^{2^n-1}$ and analysing infinitesimal unitary actions through Lie-algebra directions. We introduce Classical-to-Lie-algebra (CLA) maps and the criterion of almost Complete Local Selectivity (aCLS), which combines directional completeness with data-dependent local selectivity. Within this framework, we show that data-independent trainable unitaries are complete but non-selective, i.e. learnable rigid reorientations, whereas pure data encodings are selective but non-tunable, i.e. fixed deformations. Hence, geometric flexibility requires a non-trivial joint dependence on data and trainable weights. We further show that accessing high-dimensional deformations of many-qubit state manifolds requires parametrised entangling directions; fixed entanglers such as CNOT alone do not provide adaptive geometric control. Numerical examples validate that aCLS-satisfying data re-uploading models outperform non-tunable schemes while requiring only a quarter of the gate operations. Thus, the resulting picture reframes QNN design from state reachability to controllable geometry of hidden quantum representations.

Recent studies show that quantum neural networks (QNNs) generalize well in few-shot regimes. To extend this advantage to large-scale tasks, we propose Q-LoRA, a quantum-enhanced fine-tuning scheme that integrates lightweight QNNs into the low-rank adaptation (LoRA) adapter. Applied to AI-generated content (AIGC) detection, Q-LoRA consistently outperforms standard LoRA under few-shot settings. We analyze the source of this improvement and identify two possible structural inductive biases from QNNs: (i) phase-aware representations, which encode richer information across orthogonal amplitude-phase components, and (ii) norm-constrained transformations, which stabilize optimization via inherent orthogonality. However, Q-LoRA incurs non-trivial overhead due to quantum simulation. Motivated by our analysis, we further introduce H-LoRA, a fully classical variant that applies the Hilbert transform within the LoRA adapter to retain similar phase structure and constraints. Experiments on few-shot AIGC detection show that both Q-LoRA and H-LoRA outperform standard LoRA by over 5% accuracy, with H-LoRA achieving comparable accuracy at significantly lower cost in this task.

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific resource constraints. Distinct from broader quantum machine learning, QDL emphasizes compositional depth at the pipeline level and the integration of quantum or quantum-inspired components within end-to-end workflows. This review provides an operational definition of QDL and introduces a taxonomy comprising four primary paradigms: hybrid quantum-classical models, quantum deep neural networks, quantum algorithms for deep learning primitives, and quantum-inspired classical algorithms. Theoretical principles are connected to advanced architectures, software toolchains, and experimental demonstrations across superconducting, trapped-ion, photonic, semiconductor spin, and neutral-atom systems, as well as quantum annealers. Claims of quantum advantage are critically assessed by distinguishing provable complexity-theoretic separations from empirical observations. The analysis characterizes trade-offs between model expressivity, trainability, and classical simulability, while systematically detailing the bottlenecks imposed by optimization landscapes, input-output access models, and hardware constraints. Applications are surveyed in domains encompassing image classification, natural language processing, scientific discovery, quantum data processing, and quantum optimal control, underscoring fair benchmarking against optimized classical counterparts and a comprehensive assessment of resource requirements. This review serves as a tutorial entry point for graduate students while guiding readers to specialized literature. It concludes with a verification-aware roadmap to transition QDL from near-term demonstrations to scalable and fault-tolerant implementations.

We introduce a sequence modeling framework in which the latent state is a complex-valued wave function evolving on a finite-dimensional Hilbert space under a learned, time-dependent Hamiltonian. Unlike standard recurrent architectures that rely on gating mechanisms to suppress competing hypotheses, our framework utilizes quantum interference: the Hamiltonian steers the phases of complex amplitudes so that conflicting interpretations cancel while compatible ones reinforce. The dynamics are strictly unitary, ensuring that the state norm is preserved exactly at every time step via a Cayley (Crank--Nicolson) discretization. Token probabilities are extracted using the Born rule, a quadratic measurement operator that couples magnitudes and relative phases. Our primary theoretical contribution is a separation theorem characterizing the representational advantage of this readout: we define a family of disambiguation tasks that a complex unitary model of dimension $N$ solves exactly, but which requires a state dimension of $Ω(N^2)$ for any real-valued orthogonal model equipped with a standard affine-softmax readout. This quadratic gap arises because the Born rule implicitly lifts the $N$-dimensional state into the space of rank-one Hermitian matrices, accessing pairwise phase correlations that are inaccessible to linear projections. Finally, we derive a continuity equation for the latent probability mass, yielding conserved pairwise currents that serve as a built-in diagnostic for tracing information flow between dimensions.

This work presents a formulation to express and optimize stochastic neural networks as quantum circuits in gate-based quantum computing. Motivated by a classical perceptron, stochastic artificial neurons are introduced and combined into a quantum neural network. The Kiefer-Wolfowitz algorithm in combination with simulated annealing is used for training the network weights. Several topologies and models are presented, including shallow fully connected networks, Hopfield Networks, Restricted Boltzmann Machines, Autoencoders and convolutional neural networks. We also demonstrate the combination of our optimized neural networks as an oracle for the Grover algorithm to realize a quantum generative AI model.

Circuit cutting decomposes a large quantum circuit into smaller subcircuits executed independently; expectation values are recovered by classically combining subcircuit outcomes. Prior work characterises cutting overhead via subcircuit counts and sampling complexity, but its end-to-end impact on iterative, estimator-driven training pipelines remains under-measured from a systems perspective. We propose DistributedEstimator, a cut-aware estimator execution pipeline that treats circuit cutting as a staged distributed workload, instrumenting each query across four phases: partitioning, subexperiment generation, parallel execution, and classical reconstruction. Using logged runtime traces and learning outcomes on two binary classification workloads (Iris and MNIST), we quantify cutting overheads, scaling limits, and sensitivity to injected stragglers, and assess whether accuracy and robustness are preserved under matched training budgets. Reconstruction dominates per-query time -- a median of 53% and 95th percentile of 58% at three cuts -- bounding achievable speed-up under parallelism. Despite this, test accuracy is fully preserved on Iris and maintained without systematic degradation on MNIST across all cut configurations. Robustness under Gaussian noise and FGSM perturbations is similarly preserved, with several configurations matching or improving on the uncut baseline. Exponential growth of subexperiment counts (${O}(9^c)$ for CNOT-based decomposition) is a fundamental barrier limiting practical experimentation to small qubit counts. These results establish that practical scaling for learning workloads requires reducing and overlapping reconstruction, scheduling policies for barrier-dominated critical paths, and computationally efficient reconstruction strategies for larger qubit counts.

Graph neural networks (GNNs) are a powerful framework for learning representations from graph-structured data, but their direct implementation on near-term quantum hardware remains challenging due to circuit depth, multi-qubit interactions, and qubit scalability constraints. In this work, we introduce a hybrid quantum graph learning architecture designed explicitly for unsupervised learning in the noisy intermediate-scale quantum (NISQ) regime. Our approach combines a variational quantum feature extraction layer with an edge-local and qubit-efficient quantum message-passing mechanism inspired by the Quantum Alternating Operator Ansatz (QAOA) framework. The message-passing operation is decomposed into pairwise interactions along graph edges using standard single- and two-qubit gates. For a graph with $N$ nodes and $n$-qubit feature registers, this reduces the number of qubits required at one time from $Nn$ to at most $2n$. We train the model using the Deep Graph Infomax objective to perform unsupervised node representation learning. The external class labels are not used during graph construction or training and are used only to evaluate the learned embeddings. Experiments on the Cora citation network and the Phase 3 release of the 1000 Genomes Project show that the quantum edge interaction contributes to the quality of the learned node representations.

We propose a variational quantum implementation of self-attention (QSA)-the core operation in transformers and large language models-which predicts future elements of a sequence by forming overlap-weighted combinations of past data. At variance with previous approaches, our QSA realizes the required nonlinearity through interference of state overlaps and a degree-$k$ polynomial kernel, and estimates a loss based on Rényi-$1/2$ entropic functionals via two observables' expectation values, avoiding the decoding of amplitude-encoded predictions into classical probabilities. QSA also accommodates a constrained, trainable data-embedding tying state overlaps to data-level similarities. Its dominant end-to-end training complexity scales as $O\left(μ^{-1}k^2Td\right)$, versus $O\left(T d^{k+1}\right)$ of the fairest classical comparison, with $μ$ a training signal; we show numerically that this allows a complexity advantage in the regime where sequence length $T$ dominates the embedding size $d$. In simulations, our QSA-based quantum transformer learns sequence prediction on classical data and on many-body transverse-field Ising trajectories-establishing trainable attention as a practical primitive for quantum dynamical modeling.

With increasing life expectancy, AD has become a major global health concern. While classical AI-based methods have been developed for early diagnosis and stage classification of AD, growing data volumes and limited computational resources necessitate faster, more efficient approaches. Quantum-based AI methods, which leverage superposition and entanglement principles along with high-dimensional Hilbert space, can surpass classical approaches' limitations and offer higher accuracy for high-dimensional, heterogeneous, and noisy data. In this study, a Quantum-Based Parallel Model (QBPM) architecture is proposed for the efficient classification of AD stages using MRI datasets, inspired by the principles of classical model parallelism. The proposed model leverages quantum advantages by employing two distinct quantum circuits, each incorporating rotational and entanglement blocks, running in parallel on the same quantum simulator. The classification performance of the model was evaluated on two different datasets to assess its overall robustness and generalization capability. The proposed model demonstrated high classification accuracy across both datasets, highlighting its overall robustness and generalization capability. Results obtained under high-level Gaussian noise, simulating real-world conditions, further provided experimental evidence for the model's applicability not only in theoretical but also in practical scenarios. Moreover, compared with five different classical transfer learning methods, the proposed model demonstrated its efficiency as an alternative to classical approaches by achieving higher classification accuracy and comparable execution time while utilizing fewer circuit parameters. The results indicate that the proposed QBPM architecture represents an innovative and powerful approach for the classification of stages in complex diseases such as Alzheimer's.

Quantum implicit neural representations have recently emerged as compact function approximators for continuous visual signals. In parallel, Neural Radiance Fields (NeRFs) have become a dominant framework for novel-view synthesis by recovering continuous volumetric scene representations from posed 2D images, but often require substantial model capacity and intensive optimisation. We introduce 3D Quantum Implicit Scene Representation (3D-QISR), the first hybrid quantum-classical radiance-field model for novel-view synthesis from 2D observations. 3D-QISR replaces the classical NeRF backbone with parameterised quantum circuits that encode spatial and view-dependent information through quantum state transformations, enabling compact quantum-enhanced implicit representations while preserving compatibility with standard volumetric rendering. We propose two architectures: Full 3D-QISR, which maximises the representational role of a unified quantum state, and Dual-Branch 3D-QISR, which separates spatial and view-dependent quantum embeddings to introduce a task-aligned inductive bias, reduce state-preparation complexity, and improve scalability and hardware compatibility. Experiments on moderate-resolution novel-view synthesis benchmarks show that 3D-QISR executed on simulated quantum hardware matches or outperforms classical baselines while using fewer than half the trainable parameters. These results position quantum neural networks as compact and competitive building blocks for continuous volumetric scene representation, opening a new direction for quantum-enhanced implicit neural rendering.

Quantum machine learning has emerged as a promising application domain for near-term quantum hardware, particularly through hybrid quantum-classical models that leverage both classical and quantum processing. Although numerous hybrid architectures have been proposed and demonstrated successfully on benchmark tasks, a significant open question remains regarding the specific contribution of quantum components to the overall performance of these models. In this work, we aim to shed light on the impact of quantum processing within hybrid quantum-classical neural network architectures through a rigorous statistical study under ideal, noise-free simulation. We systematically assess a selection of commonly used HQNN architectures on three binary medical classification tasks covering medical signal data as well as planar and volumetric images. In doing so, we examine the influence attributable to classical and quantum aspects such as encoding schemes, entanglement, and circuit size. Within this experimental setting, we find that in best-case scenarios, hybrid models show performance comparable to their classical counterparts. However, in most cases, performance metrics deteriorate when the investigated QNN components replace matched classical processing layers. Our multi-modal analysis provides empirical insights into the contributions of the tested quantum components and advocates for cautious claims and design choices for hybrid models in near-term applications.

Quantum data re-uploading has proved powerful for classical inputs, where repeatedly encoding features into a small circuit yields universal function approximation. Extending this idea to quantum inputs remains underexplored, as the information contained in a quantum state is not directly accessible in classical form. We propose and analyze a quantum data re-uploading architecture in which a qubit interacts sequentially with fresh copies of an arbitrary input state. The circuit can approximate any bounded continuous function using only one ancilla qubit and single-qubit measurements, provided that sufficiently many copies of the input state and, in general, sufficiently many layers are available. By alternating entangling unitaries with mid-circuit resets of the input register, the architecture realizes a discrete cascade of completely positive and trace-preserving maps, analogous to collision models in open quantum system dynamics. Our framework provides a space-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.

Neuromorphic and quantum computing have recently emerged as promising paradigms for advancing artificial intelligence, each offering complementary strengths. Neuromorphic systems built on spiking neurons excel at processing time series data efficiently through sparse, event-driven computation, consuming energy only upon input events. Quantum computing, on the other hand, operates on state spaces that grow exponentially in dimension with the number of qubits -- as a consequence of tensor-product composition -- with quantum states admitting superposition across basis states and entanglement between subsystems. Hybrid approaches combining these paradigms have begun to show potential, but existing quantum spiking models have important limitations. Notably, they implement classical memory mechanisms on single qubits, requiring repeated measurements to estimate firing probabilities, while relying on conventional backpropagation for training. In this paper, we propose a novel stochastic quantum spiking (SQS) neuron model that addresses these challenges. The SQS neuron uses multi-qubit quantum circuits to realize a spiking unit with internal quantum memory, enabling event-driven probabilistic spike generation in a single shot during inference. Furthermore, we study networks of SQS neurons, dubbed SQS neural networks (SQSNN), and demonstrate that they can be trained via a hardware-friendly local learning rule, eliminating the need for global classical backpropagation. The proposed SQSNN model is shown via experiments with both conventional and neuromorphic datasets to improve over previous quantum spiking neural networks, as well as over classical counterparts, when fixing the overall number of trainable parameters, highlighting its potential for event-driven applications such as neuromorphic integrated sensing and communications (N-ISAC).

In this work, a novel algorithm structured on Lie algebras for the approximate quantum state preparation problem is proposed, addressing a challenge of fundamental importance in many areas of quantum computing. The algorithm uses a variational quantum circuit designed on the Standard Recursive Block Basis (SRBB), a hierarchical construction for the matrix algebra of the $SU(2^n)$ group, which is capable of linking the variational parameters with the topology of the Lie group. Compared to the full algebra, using only diagonal components reduces the number of CNOTs by an exponential factor, as well as the circuit depth, in full agreement with the relaxation principle inherent to the approximation methodology of minimizing resources while achieving high accuracy. The desired quantum state is then approximated by a novel quantum neural network, which is designed based on the diagonal SRBB sub-algebra. This approach provides a new scheme for approximate quantum state preparation in a variational framework and a specific use case for the SRBB hierarchy. The performance of the algorithm is assessed with different loss functions, such as fidelity, trace distance, and Frobenius norm, in relation to two optimizers: Adam and Nelder-Mead. The results highlight the potential of SRBB in close connection with the geometry of unitary groups, achieving high accuracy of up to 4 qubits in simulation, but also its current limitations with an increasing number of qubits. Additionally, the approximate SRBB-based QSP algorithm has been tested on real quantum devices to assess its performance with a small number of qubits.