In this work, we present a training method for a Fully Quantum Neural Network (FQNN) based entirely on quantum circuits. The model processes data exclusively through quantum operations, without incorporating classical neural network layers. In the proposed architecture, the roles of classical neurons and weights are assumed, respectively, by qubits and parameterized quantum gates: input features are encoded into quantum states of qubits, while the network weights correspond to the rotation angles of quantum gates that govern the system’s state evolution. The optimization of gate parameters is performed using directional gradient estimation, where gradients are numerically approximated via finite differences, eliminating the need for analytic derivation. The training objective is defined as the quantum-state fidelity, which measures the similarity between the network’s output state and a reference state representing the correct class. Experiments were conducted using the Qiskit AerSimulator, which allows for the accurate simulation of quantum circuits on a classical computer. The proposed approach was applied to the classification of the Iris dataset. The experimental results demonstrate that the FQNN is capable of effectively learning to distinguish between classes based on input features, achieving stable test accuracy across runs. These findings confirm the feasibility of constructing fully quantum classifiers without relying on hybrid quantum—classical architectures. The FQNN architecture consists of multiple quantum layers, each incorporating parameterized rotation operations and entanglement between qubits. The number of layers is determined by the ratio of quantum parameters (weights) to the number of input features. Each layer functions analogously to a hidden layer in a classical neural network, transforming the quantum-state space into a richer feature representation through controlled quantum operations. As a result, the network is capable of dynamically modeling dependencies among input features without the use of classical activation functions.
In this work, we present a training method for a Fully Quantum Neural Network (FQNN) based entirely on quantum circuits. The model processes data exclusively through quantum operations, without incorporating classical neural network layers. In the proposed architecture, the roles of classical neurons and weights are assumed, respectively, by qubits and parameterized quantum gates: input features are encoded into quantum states of qubits, while the network weights correspond to the rotation angles of quantum gates that govern the system’s state evolution. The optimization of gate parameters is performed using directional gradient estimation, where gradients are numerically approximated via finite differences, eliminating the need for analytic derivation. The training objective is defined as the quantum-state fidelity, which measures the similarity between the network’s output state and a reference state representing the correct class. Experiments were conducted using the Qiskit AerSimulator, which allows for the accurate simulation of quantum circuits on a classical computer. The proposed approach was applied to the classification of the Iris dataset. The experimental results demonstrate that the FQNN is capable of effectively learning to distinguish between classes based on input features, achieving stable test accuracy across runs. These findings confirm the feasibility of constructing fully quantum classifiers without relying on hybrid quantum—classical architectures. The FQNN architecture consists of multiple quantum layers, each incorporating parameterized rotation operations and entanglement between qubits. The number of layers is determined by the ratio of quantum parameters (weights) to the number of input features. Each layer functions analogously to a hidden layer in a classical neural network, transforming the quantum-state space into a richer feature representation through controlled quantum operations. As a result, the network is capable of dynamically modeling dependencies among input features without the use of classical activation functions.
This research explores the integration of quantum computing with classical machine learning to enhance data classification tasks using Quantum Neural Networks (QNN) and Parameterized Quantum Circuits (PQC). The hybrid approach leverages the advantages of both quantum and classical systems to improve the efficiency and accuracy of data processing. In this model, data is encoded into qubits using amplitude encoding, representing input vectors as amplitudes of quantum states. The QNN is initialized by placing the qubits in superposition using Hadamard gates, followed by data encoding with parameterized rotational gates that map classical data to quantum states using rotation angles. PQC plays a central role by applying layers of parameterized quantum operations to process data in the quantum space. These parameters are optimized during the training process, where a quadratic loss function minimizes the error between the predicted quantum states and the true class labels using gradient descent. Experiments conducted on the MNIST dataset show that the hybrid the hybrid quantum-classical neural network (QCNN) with PQC achieves a classification accuracy of over 95%, highlighting its potential in machine learning applications. The results demonstrate that integrating quantum computing with classical machine learning enhances performance in complex data analysis tasks due to the exponential growth of quantum state space and the parallelism of quantum systems, making hybrid models promising for computer vision and classification tasks.
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.
This paper presents a hybrid quantum-classical machine learning model for classification tasks, integrating a 4-qubit quantum circuit with a classical neural network. The quantum circuit is designed to encode the features of the Iris dataset using angle embedding and entangling gates, thereby capturing complex feature relationships that are difficult for classical models alone. The model, which we term a Quantum Convolutional Neural Network (QCNN), was trained over 20 epochs, achievinga perfect 100% accuracy on the Iris dataset test set on 16 epoch. Our results demonstrate the potential of quantum-enhanced models in supervised learning tasks, particularly in efficiently encoding and processing data using quantum resources. We detail the quantum circuit design, parameterizedgate selection, and the integration of the quantum layer with classical neural network components.This work contributes to the growing body of research on hybrid quantum-classical models and theirapplicability to real-world datasets.
One of the biggest problems is imbalanced data classification in machine learning. The minority class is usually represented less often, causing biased predictions and a lack of generalizability. The traditional machine learning models and deep learning models maximize the overall accuracy, which results in the accuracy paradox, and the minority class detection is weak in applications like fraud detection, medical diagnosis, or anomaly detection. In order to overcome the above drawbacks, the hybrid Quantum Neural Network (QNN) learning system for imbalanced data is suggested in this paper. The proposed framework is a hybrid between classical data preprocessing and a variational quantum circuit architecture, in which the input features are encoded into qubits via angle encoding, and then processed within a layer of parameterized quantum circuits, and the output features are mapped by measurement. To enhance minority class learning in optimization, a weighted cross-entropy loss function is used. The model is tested on an imbalanced dataset and compared with several basic models, including Artificial Neural Networks (ANN), Support Vector Machines (SVM), Random Forest, XGBoost, and LightGBM. The experimental results show the improvements in minority class recall and F1-scores, achieving an overall accuracy of 94.3%, and a 7%-10% higher F1-score than baseline approaches. The results suggest that QNN-based architectures may be a suitable solution to improve the classification performance in imbalanced learning environments.
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.
Quantum machine learning is emerging as a strategy to solve real-world problems. As a quantum computing model, parameterized quantum circuits provide an approach for constructing quantum machine learning algorithms, which may either realize computational acceleration or achieve better algorithm performance than classical algorithms. Based on the parameterized quantum circuit, we propose a hybrid quantum-classical convolutional neural network (HQCCNN) model for image classification that comprises both quantum and classical components. The quantum convolutional layer is designed using a parameterized quantum circuit. It is used to perform linear unitary transformation on the quantum state to extract hidden information. In addition, the quantum pooling unit is used to perform pooling operations. After the evolution of the quantum system, we measure the quantum state and input the measurement results into a classical fully connected layer for further processing. We demonstrate its potential by applying HQCCNN to the MNIST dataset. Compared to a convolutional neural network in a similar architecture, the results reveal that HQCCNN has a faster training speed and higher testing set accuracy than a convolutional neural network.