Exploration of Quantum Machine Learning: Comparative Study of Hybrid VQC and Quantum Kernel SVM for Binary Classification

This article focuses on the field of quantum machine learning, comparing the performance of hybrid variational quantum circuits (VQC) and quantum kernel support vector machines (QSVM) in binary classification tasks. The project is implemented using the PyTorch and PennyLane frameworks, aiming to reveal the advantages, disadvantages, and applicable scenarios of the two methods, providing a reference for understanding the current state of quantum machine learning.

The performance of classical computers once improved following Moore's Law, but silicon-based chips approaching physical limits have slowed down the growth of computing power. Problems such as large integer factorization and quantum simulation remain challenges for classical computing. Quantum computing leverages properties like superposition and entanglement to achieve exponential acceleration on specific problems. Quantum machine learning (QML), as an interdisciplinary field, has shown unique potential.

Basic Concepts: Qubits (superposition state), quantum gates (operation units such as Pauli-X, Hadamard), parameterized quantum circuits (with trainable parameters). Project Objectives: Compare the performance of VQC and QSVM in binary classification tasks, using the PyTorch and PennyLane frameworks, and analyze their advantages, disadvantages, and applicable scenarios.

Core Ideas: Encode classical data into quantum states → process via parameterized quantum circuits → measure to get classical results → adjust parameters via classical optimization. Technical Implementation: Data encoding layer (angle encoding, etc.), variational layer (parameterized quantum gate loops), entanglement layer (CNOT gates), measurement layer (map expectation values to categories). Optimization Strategies: Parameter shift rule (gradient estimation), finite difference method (lower precision).

Core Ideas: Use quantum circuits to implement high-dimensional mapping, enhancing the classification ability of classical SVM. Technical Implementation: Quantum feature mapping (data → quantum state), quantum kernel function calculation (inner product), classical SVM training. Advantages: Theoretically can map to exponentially high-dimensional spaces, capturing patterns that classical kernels cannot handle.

Dataset: Iris subset or artificial non-linearly separable dataset (preprocessing: standardization, dimensionality reduction). Evaluation Metrics: Accuracy, training convergence speed, parameter sensitivity, circuit depth. Comparison Results: VQC has strong expressive power but is prone to gradient vanishing during training; QSVM training is stable but has limited expressive power; VQC has higher hardware requirements, while QSVM has better interpretability.

Technical Challenges: Quantum noise (interference in the NISQ era), limited number of qubits, non-convex optimization problems, low data encoding efficiency. Application Prospects: Fields such as quantum chemistry, financial modeling, optimization problems, pattern recognition; short-term focus on hybrid classical-quantum methods; hardware advancements will drive practical applications.

Conclusions: VQC and QSVM each have their own strengths and weaknesses (VQC has strong expressiveness but complex training; QSVM is stable but has limited expressiveness). Future research can explore combined methods or new algorithms. Recommendations: Researchers need to master frameworks like PennyLane/Qiskit, understand the mathematical foundations of quantum algorithms, and follow hardware developments; they also need a solid foundation in classical ML, knowledge of quantum physics, and interdisciplinary insight.