Towards Fault-Tolerant Quantum Deep Learning: Designing and Analyzing Quantum ResNet and Transformer with Quantum Arithmetic and Linear Algebra Primitives
Achieving a practical quantum speedup for deep neural networks (DNNs) remains a central yet elusive goal, hindered by the dual challenges of constructing deep architectures and the prohibitive overhead of data loading and measurement. We introduce a framework to overcome these barriers, specifically targeting an asymptotic speedup with respect to the large input dimensions of modern DNNs (e.g., sequence length or image size). Our framework enables the design of multi-layer Quantum ResNet and Quantum Transformer models by strategically decomposing tasks: computationally intensive operations on the large input dimension are assigned to quantum linear algebra subroutines, while operations on the smaller, fixed feature dimension are handled by efficient quantum arithmetic. A cornerstone of our approach is a novel data transfer protocol, Discrete Chebyshev Decomposition (DCD), which facilitates this modularity. Numerical validation reveals a pivotal insight: the measurement cost required to maintain a target accuracy scales sublinearly with the input dimension. This sublinear scaling is the key to preserving the quantum advantage, ensuring that I/O overhead does not nullify the computational gains. A rigorous resource analysis further corroborates the superiority of our models in both efficiency and flexibility. Powered by this targeted acceleration strategy and the efficiency of DCD, our framework establishes a viable path toward scalable quantum deep learning.
Achieving a practical quantum speedup for deep neural networks (DNNs) remains a central yet elusive goal, hindered by the dual challenges of constructing deep architectures and the prohibitive overhead of data loading and measurement. We introduce a framework to overcome these barriers, specifically targeting an asymptotic speedup with respect to the large input dimensions of modern DNNs (e.g., sequence length or image size). Our framework enables the design of multi-layer Quantum ResNet and Quantum Transformer models by strategically decomposing tasks: computationally intensive operations on the large input dimension are assigned to quantum linear algebra subroutines, while operations on the smaller, fixed feature dimension are handled by efficient quantum arithmetic. A cornerstone of our approach is a novel data transfer protocol, Discrete Chebyshev Decomposition (DCD), which facilitates this modularity. Numerical validation reveals a pivotal insight: the measurement cost required to maintain a target accuracy scales sublinearly with the input dimension. This sublinear scaling is the key to preserving the quantum advantage, ensuring that I/O overhead does not nullify the computational gains. A rigorous resource analysis further corroborates the superiority of our models in both efficiency and flexibility. Powered by this targeted acceleration strategy and the efficiency of DCD, our framework establishes a viable path toward scalable quantum deep learning.
Powerful generative artificial intelligence from large language models (LLMs) harnesses extensive computational resources for inference. In this work, we investigate the transformer architecture, a key component of these models, under the lens of fault-tolerant quantum computing. We develop quantum subroutines to construct the building blocks in the transformer, including the self-attention, residual connection with layer normalization, and feed-forward network. As an important subroutine, we show how to efficiently implement the Hadamard product and element-wise functions of matrices on quantum computers. Our algorithm prepares an amplitude encoding of the transformer output, which can be measured for prediction or use in the next layer. We find that the matrix norm of the input sequence plays a dominant role in the quantum complexity. With numerical experiments on open-source LLMs, including for bio-informatics applications, we demonstrate the potential of a quantum speedup for transformer inference in practical regimes.
Abstract Fault-tolerant quantum neural networks (QNNs) require architectures that balance learning capability with stringent non-Clifford resource constraints. This work proposes an arithmetic-aware QNN architecture that integrates a validity-controlled binary-coded decimal (BCD)-to-Excess-3 transformation as a fault-tolerant preprocessing stage prior to variational learning. The arithmetic module is realized entirely within the Clifford+T gate set and incorporates explicit BCD validity detection, enabling conditional arithmetic execution while introducing only four additional T / T † gates beyond the underlying arithmetic core. The proposed architecture is combined with a COBYLA-optimized variational ansatz and compared against a baseline QNN of identical trainable complexity. While both models achieve identical classification accuracy of 100% on the benchmark single-digit task, the arithmetic-aware architecture demonstrates superior robustness under realistic hardware noise, achieving a robustness integral of 0.080 compared to 0.071 for the baseline model. Furthermore, curvature analysis reveals a substantially flatter optimization landscape, reducing the mean curvature from 36.85 to 27.21 and indicating that the arithmetic transformation acts as an effective inductive bias that stabilizes the learning process. To evaluate scalability, an additional four-class multi-digit (00–99) classification experiment was conducted, achieving an overall accuracy of 70%. These results demonstrate that fault-tolerant arithmetic preprocessing can enhance QNN robustness and stability while maintaining bounded non-Clifford overhead, highlighting the potential of arithmetic-aware representations for robust quantum machine learning.
Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging this gap by presenting the first fully-coherent quantum implementation of a multilayer neural network with non-linear activation functions. Our constructions mirror widely used deep learning architectures based on ResNet, and consist of residual blocks with multi-filter 2D convolutions, sigmoid activations, skip-connections, and layer normalizations. We analyse the complexity of inference for networks under three quantum data access regimes. Without any assumptions, we establish a quadratic speedup over classical methods for shallow bilinear-style networks. With efficient quantum access to the weights, we obtain a quartic speedup over classical methods. With efficient quantum access to both the inputs and the network weights, we prove that a network with an N-dimensional vectorized input, k residual block layers, and a final residual-linear-pooling layer can be implemented with an error of ε with O(polylog(N/ε)k) inference cost.
Quantum machine learning (QML) is promising for potential speedups and improvements in conventional machine learning (ML) tasks (e.g., classification/regression). The search for ideal QML models is an active research field. This includes identification of efficient classical-to-quantum data encoding scheme, construction of parametric quantum circuits (PQC) with optimal expressivity and entanglement capability, and efficient output decoding scheme to minimize the required number of measurements, to name a few. However, most of the empirical/numerical studies lack a clear path towards scalability. Any potential benefit observed in a simulated environment may diminish in practical applications due to the limitations of noisy quantum hardware (e.g., under decoherence, gate-errors, and crosstalk). We present a scalable quantum-classical hybrid deep neural network (DeepQMLP) architecture inspired by classical deep neural network architectures. In DeepQMLP, stacked shallow Quantum Neural Network (QNN) models mimic the hidden layers of a classical feed-forward multi-layer perceptron network. Each QNN layer produces a new and potentially rich representation of the input data for the next layer. This new representation can be tuned by the parameters of the circuit. Shallow QNN models experience less decoherence, gate errors, etc. which make them (and the network) more resilient to quantum noise. We present numerical studies on a variety of classification problems to show the trainability of DeepQMLP. We also show that DeepQMLP performs reasonably well on unseen data and exhibits greater resilience to noise over QNN models that use a deep quantum circuit. DeepQMLP provided up to 25.3% lower loss and 7.92% higher accuracy during inference under noise than QMLP.
Nowadays, with the discovery of the power and potential of quantum computers, developing and understanding quantum-based deep learning models has become an important research area. This study investigates Quantum Transfer Learning and Quantum Hybrid Learning models that involve feature extraction and training processes using Convolutional Neural Networks (CNN) and Vision Transformer (ViT). The study aims to explore the potential advantages and differences of quantum deep learning techniques. It is envisioned that quantum computing can provide significant advantages in terms of computational speed and efficiency, especially in complex and large-scale data sets. Therefore, this study will contribute to a better understanding of the practical applications and potential impacts of quantum deep learning techniques. In this study, we evaluate the performance of four different quantum deep learning architectures using two different datasets. The classifiers used are the pre-trained ResNet-50 with a kernel size of 5x5 and the state-of-the-art CaiT-24-XXS-224 (CaiT) transducers. Optimization was performed with Adam optimizer using the cross entropy loss function. A total of eight models were trained, each with ten iterations. Accuracy (Acc), balanced accuracy (BA), overall F𝛽 (F_beta) macro score F1 and F2, Matthew's Correlation Coefficient (MCC), sensitivity (Sens) and specificity (Spec) were used as performance measures.
Quantum attention mechanisms integrate parameterised quantum circuits or quantum linear algebra primitives into transformer architectures, drawing on superposition and entanglement in the attention computation. The field has produced more than two dozen proposals between 2022 and 2026, spanning Parameterised Quantum Circuits (PQC) on near-term hardware, Quantum Linear Algebra (QLA) on fault-tolerant hardware, and quantum annealing. This survey contributes a refined taxonomy with an attention-semantics dimension distinguishing pairwise from holistic mechanisms; a resource-realism analysis that states the measurement-overhead cost of pairwise quantum attention in the Noisy Intermediate-Scale Quantum (NISQ) regime as a proposition under explicit assumptions, with the architecture classes falling outside those assumptions identified, organised within a four-axis design framework covering sequence and qubit scaling, circuit depth, encoding overhead, and hardware platform constraints, complementing the dedicated measurement-overhead analysis; and a critical synthesis of the empirical literature that finds parity or task-conditional modest gains rather than uniform quantum advantage across the five papers reporting parameter-matched classical baselines. Six open directions are identified for the next phase of research. The survey clarifies what the current literature does and does not establish about quantum attention’s practical advantage over efficient classical alternatives.