We implement a quantum neural network on trapped-ion and IBM superconducting quantum computers for Modified National Institute of Standards image classification. Feedforward is realized through qubit rotations conditioned on measurement outcomes from previous layers. The network is trained classically, while inference is performed experimentally on quantum hardware. A tunable interpolation parameter connects the classical and quantum regimes. Moderate values improve classification performance by introducing measurement uncertainty. For borderline images misclassified classically but correctly identified quantum mechanically, we observe strong deviations from idealized simulations due to physical noise, consistent with fluctuations between nearby minima in the classification landscape. We further benchmark noise by inserting additional single- and two-qubit gate pairs into the circuits. Our results motivate more complex quantum neural networks on noisy intermediate-scale quantum devices and suggest a possible route toward classically nonsimulable architectures.
We implement a quantum neural network on trapped-ion and IBM superconducting quantum computers for Modified National Institute of Standards image classification. Feedforward is realized through qubit rotations conditioned on measurement outcomes from previous layers. The network is trained classically, while inference is performed experimentally on quantum hardware. A tunable interpolation parameter connects the classical and quantum regimes. Moderate values improve classification performance by introducing measurement uncertainty. For borderline images misclassified classically but correctly identified quantum mechanically, we observe strong deviations from idealized simulations due to physical noise, consistent with fluctuations between nearby minima in the classification landscape. We further benchmark noise by inserting additional single- and two-qubit gate pairs into the circuits. Our results motivate more complex quantum neural networks on noisy intermediate-scale quantum devices and suggest a possible route toward classically nonsimulable architectures.
Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns have become increasingly pressing as conventional computers are soon expected to approach the physical limitations that will slow their performance improvements in the near future. For these reasons, scientists have begun to explore alternative computing platforms, like quantum computers, for training neural networks. In recent years, variational quantum circuits have emerged as one of the most successful approaches to quantum deep learning on noisy intermediate scale quantum devices. We propose a hybrid quantum-classical neural network architecture where each neuron is a variational quantum circuit. We empirically analyze the performance of this hybrid neural network on a series of binary classification data sets using a simulated IBM universal quantum computer and a state-of-the-art IBM universal quantum computer. On the simulated hardware, we observe that the hybrid neural network achieves around 10% higher classification accuracy and 20% better minimization of the cost function than an individual variational quantum circuit. On the quantum hardware, we observe that each model only performs well when the qubit and gate count is sufficiently small.
Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns have become increasingly pressing as conventional computers quickly approach physical limitations that will slow performance improvements in years to come. For these reasons, scientists have begun to explore alternative computing platforms, like quantum computers, for training neural networks. In recent years, variational quantum circuits have emerged as one of the most successful approaches to quantum deep learning on noisy intermediate scale quantum devices. We propose a hybrid quantum-classical neural network architecture where each neuron is a variational quantum circuit. We empirically analyze the performance of this hybrid neural network on a series of binary classification data sets using a simulated universal quantum computer and a state of the art universal quantum computer. On simulated hardware, we observe that the hybrid neural network achieves roughly 10% higher classification accuracy and 20% better minimization of cost than an individual variational quantum circuit. On quantum hardware, we observe that each model only performs well when the qubit and gate count is sufficiently small.
Quantum machine learning on real noisy intermediate-scale quantum (NISQ) hardware has remained largely confined to binary or few-class tasks, limited by the cost of on-hardware training and the underuse of large devices at inference. We present a unified framework that classifies ten-class MNIST end-to-end on a 127-qubit IBM Eagle processor, with three central contributions. First, a two-phase protocol decouples a gradient-based classical optimization of the encoder and readout from a gradient-free optimization of the quantum parameters, removing the parameter-shift gradient cost that makes on-hardware training impractical. Second, we introduce Quantum Multi-Programming to a trained quantum classifier for the first time, packing multiple circuit copies onto one device to deliver parallel inference at no mean-accuracy cost while cutting quantum-processor job submissions proportionally. Third, a controlled comparison shows that on-hardware fine-tuning yields no measurable accuracy gain, motivating a practical NISQ workflow: train on a classical simulator and reserve the hardware for inference only. Benchmarked against a matched-capacity classical network, the quantum module shows no per-parameter accuracy advantage at this scale; we therefore frame the work as a feasibility-and-workflow demonstration for multi-class quantum image classification on current hardware.
Noisy Intermediate-Scale Quantum (NISQ) devices have led to the creation of hybrid quantum-classical algorithms, which have provided an innovative design to improve classical machine learning. This article focuses on a review of Hybrid Quantum-Classical Neural Networks (H-QCNNs) in image classification, which is an emerging area that attempts to exploit the representational ability of parameterized quantum circuits (PQCs) and the proven feature extraction capabilities of classical deep learning. We empirically examine the current tendencies in architecture, such as quanvolutional networks, sequential models, and variational quantum classifiers, and critically assess their performance on standard and custom data. The literature analysis shows a large performance difference between noiseless simulation and execution on real hardware, indicating the highly problematic aspects of scaling beyond binary tasks, quantum noise, and a lack of standardized benchmarking. Moreover, we mention such innovative contributions as the small H-QNN model that offers comparable accuracy, yet meets strict NISQ requirements. Last but not least, the current review offers a systematic taxonomy of H-QCNN architectures, a comparative study of methodology options, and a clear roadmap to future research to reach a workable quantum advantage in computer vision. It is a resource to the beginners as well as a reference to the professionals working in the field, so the field would be moved to more powerful, scalable, and hardware-conscious ways of implementation.
Quantum neural networks are a popular realization of quantum machine learning. Typically, classical data is first embedded into the state vector of a quantum system. A parameterized quantum circuit (PQC) then acts on the quantum state, with its trainable parameters continuously adjusted during the optimization process. However, current quantum hardware faces challenges, such as accumulating noise with increasing circuit complexity and a limited set of native gate operations. As a result, transpiling quantum circuits to real hardware often increases the number of the required gate instructions. These factors set considerable constraints on the accuracy of quantum machine learning models. To address these limitations, we propose a novel quantum neural network architecture, termed hardware-native parameterized quantum embedding (HN-PQE). Our approach offers two key advantages: First, HN-PQE exclusively employs the native gates of IBM's current Eagle quantum processor family, ensuring that the gate count remains stable during transpilation. Second, by combining data embedding with the PQC, HN-PQE achieves a highly compact circuit design. We empirically validate our approach on two classification tasks, simulating both idealized (no hardware noise) and noisy conditions (mimicking IBM's Brisbane device). When compared to two popular quantum neural networks, HN-PQE showed similar performance in idealized scenarios but demonstrated significant noise resilience under hardware-noise conditions. This resilience makes HN-PQE a promising candidate for future quantum machine learning experiments on real hardware.
Parameterized Quantum Circuits (PQC) are promising towards quantum advantage on near-term quantum hardware. However, due to the large quantum noises (errors), the performance of PQC models has a severe degradation on real quantum devices. Take Quantum Neural Network (QNN) as an example, the accuracy gap between noise-free simulation and noisy results on IBMQ-Yorktown for MNIST-4 classification is over 60%. Existing noise mitigation methods are general ones without leveraging unique characteristics of PQC; on the other hand, existing PQC work does not consider noise effect. To this end, we present QuantumNAT, a PQC-specific framework to perform noise-aware optimizations in both training and inference stages to improve robustness. We experimentally observe that the effect of quantum noise to PQC measurement outcome is a linear map from noise-free outcome with a scaling and a shift factor. Motivated by that, we propose post-measurement normalization to mitigate the feature distribution differences between noise-free and noisy scenarios. Furthermore, to improve the robustness against noise, we propose noise injection to the training process by inserting quantum error gates to PQC according to realistic noise models of quantum hardware. Finally, post-measurement quantization is introduced to quantize the measurement outcomes to discrete values, achieving the denoising effect. Extensive experiments on 8 classification tasks using 6 quantum devices demonstrate that QuantumNAT improves accuracy by up to 43%, and achieves over 94% 2-class, 80% 4-class, and 34% 10-class classification accuracy measured on real quantum computers. The code for construction and noise-aware training of PQC is available in the TorchQuantum library.