In the era of Noisy Intermediate-Scale Quantum(NISQ), Variational Quantum Algorithm (VQA) is the most promising method to achieve quantum dominance. The VQA is a quantum classical-hybrid algorithm that typically uses a classical optimizer to train a parameterized quantum circuit (PQC). However, the barren plateau phenomenon will occur during training, reducing the training of quantum circuits. In this paper we design a quantum circuit structure, which combines the tree tensor network (TTN) and the parameterized quantum circuit, calling this circuit the tree parameterized quantum circuit (TPQC). We found that the TPQC had better expressiveness and was also effective in alleviating the barren plateau. The quantum classifier of TPQC is used for network attack intrusion detection, and compared with the quantum classifier of universal parameterized quantum circuit, we demonstrate that TPQC has higher accuracy for binary classification tasks.
In the era of Noisy Intermediate-Scale Quantum(NISQ), Variational Quantum Algorithm (VQA) is the most promising method to achieve quantum dominance. The VQA is a quantum classical-hybrid algorithm that typically uses a classical optimizer to train a parameterized quantum circuit (PQC). However, the barren plateau phenomenon will occur during training, reducing the training of quantum circuits. In this paper we design a quantum circuit structure, which combines the tree tensor network (TTN) and the parameterized quantum circuit, calling this circuit the tree parameterized quantum circuit (TPQC). We found that the TPQC had better expressiveness and was also effective in alleviating the barren plateau. The quantum classifier of TPQC is used for network attack intrusion detection, and compared with the quantum classifier of universal parameterized quantum circuit, we demonstrate that TPQC has higher accuracy for binary classification tasks.
We introduce the Tree Tensor Network-enhanced Quantum-Classical Neural Network (TTN-QNet), a hybrid architecture that leverages the hierarchical structure of Tree Tensor Networks for efficient parameter representation and Variational Quantum Circuits (VQC) for expressive modeling. Unlike Tensor Ring Networks, TTNs reduce parameter redundancy through a tree-based topology, enabling scalable and interpretable computation. The proposed TTN-QNet is evaluated on the Iris, MNIST, and CIFAR-10 datasets, achieving classification accuracies of 93.2%, 85.24%, and 81.67%, respectively, on binary classification tasks. TTN-QNet demonstrates rapid convergence and robustness against barren plateaus, offering a promising direction for deep quantum learning.
Variational Quantum Algorithms (VQAs) are being highlighted as key quantum algorithms for demonstrating quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices, which are limited to executing shallow quantum circuits because of noise. However, the barren plateau problem, where the gradient of the loss function becomes exponentially small with system size, hinders this goal. Recent studies suggest that embedding tensor networks into quantum circuits and initializing the parameters can avoid the barren plateau. Yet, embedding tensor networks into quantum circuits is generally difficult, and methods have been limited to the simplest structure, Matrix Product States (MPSs). This study proposes a method to embed Tree Tensor Networks (TTNs), characterized by their hierarchical structure, into shallow quantum circuits. TTNs are suitable for representing two-dimensional systems and systems with long-range correlations, which MPSs are inadequate for representing. Our numerical results show that embedding TTNs provides better initial quantum circuits than MPS. Additionally, our method has a practical computational complexity, making it applicable to a wide range of TTNs. This study is expected to extend the application of VQAs to two-dimensional systems and those with long-range correlations, which have been challenging to utilize.
With the advancement of quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid quantum-classical algorithms have emerged as promising approaches for addressing certain machine learning tasks. This study investigates the Variational Quantum Classifier (VQC), a hybrid model that integrates parameterized quantum circuits with classical optimization routines, implemented via IBM’s Qiskit framework. We provide a detailed account of the VQC architecture, including feature encoding, ansatz construction, and optimization methodology. To assess its performance, we conduct a comparative analysis between VQC and classical Support Vector Classifiers (SVC) across synthetic and real-world datasets, including Iris and a binary-filtered version of MNIST. Experimental results reveal that classical models consistently achieve higher accuracy and faster training times. However, the VQC demonstrates functional viability, particularly under noise-free conditions and reduced-dimensionality settings. These findings underscore the current limitations of quantum models while highlighting the potential of VQC as a proof-of-concept for quantum-enhanced learning as quantum hardware matures.
Processing data through a quantum classifier is a powerful alternative to traditional machine learning. A quantum classifier consists of a series of parameterized quantum circuits that train known quantum data to approximate classification functions and accurately classify unknown data. Considering the development limitations of quantum computers, this paper proposes a kind of lightweight quantum classifier which contains fewer circuit parameters and integrated with the classical optimization algorithm in order to achieve high-precision classification. The architecture design of quantum classifier is inspired on tensor network states such as matrix product state, tree network (TTN) and multi-scale entangled renormalization (MERA), the classical optimization algorithm adopts gradient descent (GD), particle swarm optimization (PSO) and quantum behavior improved particle swarm optimization (QPSO). The whole classical-quantum hybrid model could theoretically be implemented on near-term devices, and its performance is proved on Anderson Iris data set.
With the advancement of quantum machine learning, it has demonstrated immense potential in addressing traditionally complex problems. However, existing quantum circuit designs still exhibit limitations in expressibility and model performance. To tackle this challenge, inspired by tensor network structures, this paper proposes an Optimized Tree-Structured Entanglement Circuit (OTSEC). OTSEC employs parameterized quantum gates as fundamental circuit units to construct a hierarchical tree-structured framework for local quantum state initialization and entanglement optimization. Additionally, an Entanglement Adjustment Module (EAM) is introduced to regulate entanglement across different groups of qubits, optimizing long-range correlations and global feature fusion, thereby significantly enhancing the circuit’s expressibility.We further design an Optimized Tree-Structured Variational Quantum Classifier (OT-VQC) and apply it to network intrusion detection tasks. Simulation experiments on the KDD-CUP99 and UNSW-NB15 datasets demonstrate that OT-VQC significantly outperforms conventional variational quantum classifiers with standard circuit structures in key metrics such as classification accuracy, precision, and recall.
Abstract Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. However, the training of variational quantum circuits (VQCs) is susceptible to a phenomenon known as barren plateaus (BPs). Various approaches have been proposed to mitigate this issue, such as using neural networks to generate VQC parameters. In this paper, we improve the NN-based BP mitigation approach by refining the neural network architecture and extend its applicability to a more generalized scenario that includes random quantum inputs and VQC structures. We evaluate the effectiveness of the approach by comparing the convergence speed before and after it is utilized. Furthermore, we give an explanation for the effectiveness of the NN-based BP mitigation approach by utilizing a loss landscape visualization technique and the expressibility metric of VQC. The smoothness of the loss landscape offers an intuitive insight into the approach’s utility, while the reduction in expressibility accounts for the enhanced trainability. Our research highlights the universal applicability of the NN-based BP mitigation approach, underscoring its potential to drive progress in the development of VQAs across diverse domains.