Supervised quantum machine learning models are kernel methods

Abstract

With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "quantum models" are sometimes called "quantum neural networks", it has been repeatedly noted that their mathematical structure is actually much more closely related to kernel methods: they analyse data in high-dimensional Hilbert spaces to which we only have access through inner products revealed by measurements. This technical manuscript summarises and extends the idea of systematically rephrasing supervised quantum models as a kernel method. With this, a lot of near-term and fault-tolerant quantum models can be replaced by a general support vector machine whose kernel computes distances between data-encoding quantum states. Kernel-based training is then guaranteed to find better or equally good quantum models than variational circuit training. Overall, the kernel perspective of quantum machine learning tells us that the way that data is encoded into quantum states is the main ingredient that can potentially set quantum models apart from classical machine learning models.

26 pages, 9 figures - Version 2 emphasises focus on supervised learning, adds more references to existing literature, deletes section on state discrimination due to a technical error, and updates the comparison between kernel-based and variational training

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Cited by in corpus (43)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum machine learning beyond kernel methods
• QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer
• Quantum Machine Learning: from physics to software engineering
• Biology and medicine in the landscape of quantum advantages
• Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces
• Towards quantum enhanced adversarial robustness in machine learning
• Machine Learning for Anomaly Detection in Particle Physics
• Reflection Equivariant Quantum Neural Networks for Enhanced Image Classification
• Semiconductor Defect Detection by Hybrid Classical-Quantum Deep Learning
• Hybrid Classical-Quantum Autoencoder for Anomaly Detection
• Quantum Machine Learning for Finance
• Application of quantum machine learning using quantum kernel algorithms on multiclass neuron M type classification
• Quantum Embedding Search for Quantum Machine Learning
• Variational Quantum Anomaly Detection: Unsupervised mapping of phase diagrams on a physical quantum computer
• Fock State-enhanced Expressivity of Quantum Machine Learning Models
• Quantum Gaussian Process Regression for Bayesian Optimization
• Quantum kernels to learn the phases of quantum matter
• Quantum Convolutional Neural Networks with Interaction Layers for Classification of Classical Data
• Compact quantum kernel-based binary classifier
• Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning
• Data re-uploading with a single qudit
• Potential and limitations of random Fourier features for dequantizing quantum machine learning
• An exponentially-growing family of universal quantum circuits
• Efficient algorithms for quantum information bottleneck
• The role of entanglement for enhancing the efficiency of quantum kernels towards classification
• On exploring the potential of quantum auto-encoder for learning quantum systems
• Embedding Learning in Hybrid Quantum-Classical Neural Networks
• Quantum kernels with squeezed-state encoding for machine learning
• Semisupervised Anomaly Detection using Support Vector Regression with Quantum Kernel
• A Quantum Kernel Learning Approach to Acoustic Modeling for Spoken Command Recognition
• Photonic kernel machine learning for ultrafast spectral analysis
• Pulsar Classification: Comparing Quantum Convolutional Neural Networks and Quantum Support Vector Machines
• Qudit Machine Learning
• Application of quantum computing to a linear non-Gaussian acyclic model for novel medical knowledge discovery
• Quantum-enhanced neural networks in the neural tangent kernel framework
• Quantum Kernel Evaluation via Hong-Ou-Mandel Interference
• Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity
• Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
• Learning unitaries with quantum statistical queries
• When Quantum and Classical Models Disagree: Learning Beyond Minimum Norm Least Square
• Quantum Model-Discovery
• Hybrid model of the kernel method for quantum computers