The theory of the quantum kernel-based binary classifier

• Published in: Physics letters. A 2020-07, Vol.384 (21), p.126422, Article 126422
• Main Authors: Park, Daniel K., Blank, Carsten, Petruccione, Francesco
• Format: Article
• Language: English
• Subjects: Kernel methods; Pattern recognition; Quantum binary classification; Quantum computing; Quantum machine learning
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2020.126422

•Construction of the quantum support vector machine from the Hadamard classifier and the swap-test classifier is presented.•The essential elements of the quantum binary classifier based on the swap-test are investigated.•The quantum swap-test binary classifier is generalized to density matrix formalism and single-shot measurement.•The quantum swap-test binary classifier is extended to ensemble learning.•The Hilbert-Schmidt inner product is a symmetric and positive semi-definite kernel. Binary classification is a fundamental problem in machine learning. Recent development of quantum similarity-based binary classifiers and kernel method that exploit quantum interference and feature quantum Hilbert space opened up tremendous opportunities for quantum-enhanced machine learning. To lay the fundamental ground for its further advancement, this work extends the general theory of quantum kernel-based classifiers. Existing quantum kernel-based classifiers are compared and the connection among them is analyzed. Focusing on the squared overlap between quantum states as a similarity measure, the essential and minimal ingredients for the quantum binary classification are examined. The classifier is also extended concerning various aspects, such as data type, measurement, and ensemble learning. The validity of the Hilbert-Schmidt inner product, which becomes the squared overlap for pure states, as a positive definite and symmetric kernel is explicitly shown, thereby connecting the quantum binary classifier and kernel methods.