Quantum-enhanced least-square support vector machine: simplified quantum algorithm and sparse solutions
This work addresses improving SVM efficiency and scalability for machine learning practitioners by leveraging quantum computing, though it appears incremental as it builds on existing quantum SVM concepts.
The authors tackled the problem of enhancing least-square support vector machines (LS-SVM) with quantum algorithms, introducing a simplified quantum algorithm for matrix inversion with exponential speed-up and a hybrid quantum-classical method for sparse solutions using quantum matrix tools and kernel methods.
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion is introduced to simplify the algorithm for quantum LS-SVM, while retaining exponential speed-up. Secondly, we propose a hybrid quantum-classical version for sparse solutions of LS-SVM. By encoding a large dataset into a quantum state, a much smaller transformed dataset can be extracted using quantum matrix toolbox, which is further processed in classical SVM. We also incorporate kernel methods into the above quantum algorithms, which uses both exponential growth Hilbert space of qubits and infinite dimensionality of continuous variable for quantum feature maps. The quantum LS-SVM exploits quantum properties to explore important themes for SVM such as sparsity and kernel methods, and stresses its quantum advantages ranging from speed-up to the potential capacity to solve classically difficult machine learning tasks.