Radial basis function networks gain powerful new capabilities through the integration of quantum kernel functions, creating hybrid classical algorithms with promising applications in both interpolation and classification. QinetiQ's Emily Micklethwaite and Adam Lowe demonstrate this progress by presenting a synthetic example that validates the concept and, importantly, highlights its potential benefits over traditional support vector machines. Although kernel techniques commonly work with support vector machines, this study demonstrated that kernel-enhanced radial basis networks provide native capabilities to perform multiclass classification and have significant advantages over standard support vector machine implementations. Therefore, this work represents a step forward in leveraging quantum kernels for more general-purpose machine learning tasks and may expand the scope of quantum-enhanced algorithms.
In this work, we present synthetic examples that demonstrate the concepts for both interpolation and classification tasks, and demonstrate the potential benefits over standard kernel-based support vector machines due to the network's native ability to handle multiclass classification. The core of this work lies in encoding classical data into quantum wavefunctions, allowing the computation of kernel metrics based on the overlap of wavefunctions. To accomplish this, the team developed a method to map input data onto a Bloch sphere using rotation matrices, specifically RX gates, so that each data point occupies a unique position.
Each feature within a data point is encoded into two qubits, enabling quantum effects within the data itself. For datasets with multiple features, use an entangling unitary gate, either a CNOT gate or a random Haar unitary matrix, to create entanglement between qubits, effectively linking the features. This process results in a wave function |ψ(xi)⟩, which is used to compute the kernel matrix ＾φ using the overlap of the training data points and the selected center. The resulting kernel matrix ＾φ is composed of classical values despite being computed from a quantum wavefunction, allowing us to solve the radial basis function network using established methods. The research team demonstrated that this approach allows the calculation of kernel metrics based on the overlap of quantum wave functions, expressed as |⟨ψ(yj)|ψ(xi)⟩|², which form the basis of the kernel matrix. This breakthrough establishes a framework for integrating quantum kernels into classical machine learning algorithms and paves the way to explore performance improvements through the selection of different kernel functions, such as Gaussian and linear kernels, although this topic is reserved for future investigation.
Quantum kernel network demonstrates the potential of machine learning
In this study, we present a new implementation of quantum kernel-enhanced radial basis function networks based on established techniques used in support vector machines. Through testing on synthetic datasets, the team demonstrated that this quantum kernel radial basis function network (Q-RBF) works for both interpolation and classification tasks, achieving results comparable to existing classical machine learning methods. In particular, Q-RBF networks natively support multiclass classification, giving them potential advantages over standard support vector machine implementations. This study successfully established a proof of concept for the Q-RBF algorithm and highlighted its potential in the field of quantum machine learning. The authors acknowledge that further research is needed to fully understand the model's capabilities, especially with regard to hyperparameter optimization and practical implementation in real-world problems. Future research directions include developing and implementing this algorithm on real quantum hardware, with the aim of demonstrating feasibility for short-term quantum computing applications and investigating performance in more complex scenarios.
