The current generation of quantum computers calls for quantum algorithms that require a limited number of quantum gates and are resilient to noises. A suitable design strategy is variational circuits where parameters of circuits are determined through training, an approach that conforms with characteristics of machine learning applications. In this paper, we propose a low-depth and implementation-efficient non-linear activation function for quantum neural networks (QNNs). The building block of a quantum circuit is quantum gate which is a unitary operation. Thus, building a non-linear component out of quantum gates is challenging. While the majority of prior works used measurement as the source of non-linearity, this method has limited ability in classifying datasets. We propose a quantum circuit for the popular Rectified Linear Unit (ReLU) activation function. Our proposed circuit is based on low-cost quantum gates that can be synthesized into primitive gates in contemporary quantum computers. We exploit QNNs that rely on quantum rotation to define decision boundaries for classification problems. In addition, we use controlled quantum gates to detect correlation in data through entanglement of qubits. Our evaluations reveal that QNNs equipped with our proposed quantum ReLU perform well on standard benchmark datasets while requiring dramatically fewer number of epochs for training compared with classical neural networks. In addition, we run QNNs with different number of quantum layers on an IBM quantum computer and show that our proposed circuits are practical and generate meaningful results on real quantum computers.
The current generation of quantum computers calls for quantum algorithms that require a limited number of quantum gates and are resilient to noises. A suitable design strategy is variational circuits where parameters of circuits are determined through training, an approach that conforms with characteristics of machine learning applications. In this paper, we propose a low-depth and implementation-efficient non-linear activation function for quantum neural networks (QNNs). The building block of a quantum circuit is quantum gate which is a unitary operation. Thus, building a non-linear component out of quantum gates is challenging. While the majority of prior works used measurement as the source of non-linearity, this method has limited ability in classifying datasets. We propose a quantum circuit for the popular Rectified Linear Unit (ReLU) activation function. Our proposed circuit is based on low-cost quantum gates that can be synthesized into primitive gates in contemporary quantum computers. We exploit QNNs that rely on quantum rotation to define decision boundaries for classification problems. In addition, we use controlled quantum gates to detect correlation in data through entanglement of qubits. Our evaluations reveal that QNNs equipped with our proposed quantum ReLU perform well on standard benchmark datasets while requiring dramatically fewer number of epochs for training compared with classical neural networks. In addition, we run QNNs with different number of quantum layers on an IBM quantum computer and show that our proposed circuits are practical and generate meaningful results on real quantum computers.
A non-linear activation function is an integral component of neural network algorithms used for various tasks such as data classification and pattern recognition. In neu-romorphic/emerging-hardware-based implementations of neural network algorithms, the non-linear activation function is often implemented through dedicated analog electronics. This enables faster execution of the activation function during training and inference of neural networks compared to conventional digital implementation. Here, with a similar motivation, we propose a novel non-linear activation function that can be used in a neural network for data classification. Our activation function can be implemented by taking advantage of the inherent nonlinearity in qubit preparation and SU(2) operation in quantum mechanics. These operations are directly implementable on quantum hardware through single-qubit quantum gates as we show here. In addition, the SU(2) parameters are adjustable here making the activation function adaptable; we adjust the parameters through classical feedback like in a variational algorithm in quantum machine learning. Using our proposed quantum activation function, we report accurate classification using popular machine learning data sets like Fisher's Iris, Wisconsin's Breast Cancer (WBC), Abalone, and MNIST on three different platforms: simulations on a classical computer, simulations on a quantum simulation framework like Qiskit, and experimental implementation on quantum hardware (IBM-Q). Then we use a Bloch-sphere-based approach to intuitively explain how our proposed quantum activation function, with its adaptability, helps in data classification.
Abstract Quantum machine learning, focusing on quantum neural networks (QNNs), remains a vastly uncharted field of study. Current QNN models primarily employ variational circuits on an ansatz or a quantum feature map, often requiring multiple entanglement layers. This methodology not only increases the computational cost of the circuit beyond what is practical on near-term quantum devices but also misleadingly labels these models as neural networks, given their divergence from the structure of a typical feed-forward neural network (FFNN). Moreover, the circuit depth and qubit needs of these models scale poorly with the number of data features, resulting in an efficiency challenge for real-world machine learning tasks. We introduce a bona fide QNN model, which seamlessly aligns with the versatility of a traditional FFNN in terms of its adaptable intermediate layers and nodes, absent from intermediate measurements such that our entire model is coherent. This model stands out with its reduced circuit depth and number of requisite CNOT gates, achieving a more than 50% reduction in both compared to prevailing QNN models. Furthermore, the qubit count in our model remains unaffected by the data’s feature quantity. We test our proposed model on various benchmarking datasets such as the breast cancer diagnostic (Wisconsin) and credit card fraud detection datasets. Our model achieved an accuracy of 91% on the breast cancer dataset and 85% on the credit card fraud detection dataset, outperforming existing QNN methods by 5–10% while requiring approximately 50% fewer quantum resources. These results showcase the advantageous efficacy of our approach, paving the way for the application of quantum neural networks to relevant real-world machine learning problems.
Quantum neural networks (QNNs) have recently attracted remarkable attention as a potential alternative to classical and deep neural network (NN) models particularly under constraints imposed by noisy intermediate-scale quantum (NISQ) devices, which support only shallow circuits with few quantum bits (qubits) and limited variational depth. However, applying QNNs to natural language processing (NLP) remains challenging because text representations are typically high-dimensional, while NISQ classifiers can only encode a small number of features at a time, requiring classical compression to enable stable training and flexible circuit configuration. In addition, many existing studies integrate QNNs into rich-text representation pipelines, where the quantum circuit is often implemented as a variational quantum circuit (VQC). Here, the VQC acts as an additional component within a larger model, and it remains unclear how the quantum component improves the classification task. Therefore, in this work, we propose a fully reproducible and compact QNN pipeline that provides a controlled setting for studying the contribution of the VQC to text classification. The model is trained end-to-end with a lightweight classical compression layer, and the overall study is supported by systematic ablation analyses of the compression layer, the classifier heads under a shared frozen low-dimensional representation, and quantum circuit structure. Our model uses the term frequency-inverse document frequency (TF-IDF) features with linear compression followed by a shallow four-qubit, two-layer VQC, implemented in PyTorch and PennyLane for end-to-end training. It is evaluated on five benchmark text classification datasets against classical baselines, including logistic regression and multilayer perceptron (MLP) models. Experimental results show that the proposed QNN achieves a competitive performance across all evaluated datasets, yielding the best results on three of the five benchmark datasets.
Abstract For classification problems, ansatz circuits are an efficient and promising quantum-classical machine learning technique. However, a difficult design challenge arises: which quantum circuit should be used for model training? Low depth ansatz circuits have been used in a variety of applications in recent years. The earlier works defined several quantum circuit descriptors to evaluate an ansatz design such as the circuit expressibility, the efficiency with which a quantum circuit may exploit the Hilbert Space, and the entanglement capability, a circuit's capability of detecting data correlation. Additionally in this work, we investigate, measure, and analyze the effect of the number of ansatz repetition layers L, and the expressibility power of the data encoding module. The proposed quantum neural network classifiers were trained on four different classical datasets using 19 hardware-efficient parametrized circuits. The heuristic experimental results show that ansatz designs with high to moderate expressibiliy values outperformed ones with low expressibility values. By analyzing the circuit cost, we see a tendency toward maximizing the number of parameters which helps in the QNN model's convergence. On simulated hardware, we observe that the proposed quantum neural network achieves up to 97.5\% prediction accuracy using the angle data encoding module.
The noise of quantum-enhanced learning there is a potential of quantum-enhanced learning with noisy intermediate-scale quantum (NISQ) devices, which is limited by hardware noise and finding useful circuit architectures. In this paper, a Noise-Aware Adaptive Variational Quantum Neural Network (NAVQNN) structure is proposed, which is capable of solving such issues simultaneously. The angle encoding of classical feature vectors (variance, skewness, kurtosis, entropy) of cheque images into quantum states is done on a shallow variational circuit. The noise-sensitive adaptive ansatz generator, in turn, develops the circuit layer-by-layer by picking the new parameterized gate blocks based on their validation loss with an explicit noise model and discouraging depth and two-qubit interactions in their cost functional. The ensuing variational quantum classifier is then trained by a hybrid quantum-classical optimization cycle based on the parameter-shift rule. The experiments on the UCI banknote authentication dataset indicate the usefulness of the proposed approach with the accuracy of 0.9913, precision of 0.9869, recall of 0.9934, F1-score of 0.9902, and ROC-AUC of 0.9998. Figures of prediction score densities, decision boundary, and live inference outputs are additional proof that NAVQNN can gain a strong and well-calibrated decision-making function in compliance with practical NISQ requirements. These findings suggest that noise-conscious adaptive variational circuits can be a useful foundation for quantum-enhanced financial fraud detection and various classification problems.
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size.