The theory of the quantum kernel-based binary classifier

Abstract

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 kernelbased 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.

Support Vector Machines with Quantum State Discrimination

“…The general idea of classification algorithms based on discrimination of quantum states is also supported by recent experimental works on quantum state classification based on classical machine learning methods, such as the proposals in [9][10][11][12][13], for instance. In [14], the authors demonstrate a machine learning approach to construct a classifier of quantum states training a neural network.…”

Quantum readout error mitigation via deep learning

“…Equivalently, p is the set of diagonal elements of the final density matrix ρ produced at the end of the quantum computation. Many quantum algorithms are designed in a way that the solution to the problem is encoded in the probability distribution p. In particular, estimating an expectation value of some observable from such probability distribution is central to many NISQ algorithms, such as Variational Quantum Eigensolver (VQE) [16][17][18][19], Quantum Approximate Optimizatoin Algorithm (QAOA) [20], Quantum Machine Learning (QML) [21][22][23], and simulation of stochastic processes [24,25].…”

Facial expression recognition on a quantum computer

“…This task essentially consists in assigning a class in a given partition of a dataset to an input value, on the basis of a set of training data whose classes are known. As witnessed by the emerging of the field of Quantum Machine Learning (QML) (Wittek 2016;Schuld et al 2015;Biamonte et al 2017), Quantum Computation (Nielsen and Chuang 2011) offers a number of algorithmic techniques that can be advantageously applied for reducing the complexity of classical learning algorithms. This possibility has been variously explored for pattern classification, see e.g.…”

“…Combined with an appropriate use of quantum interference, this technique is at the base of the computational speed-up of many quantum algorithms; for example it is responsible for the exponential speed-up Fig. 1 An element of the CK+ dataset: happy face (left) and its point cloud (right) in the performance of all quantum algorithms based on the Quantum Fourier Transform (Nielsen and Chuang 2011). However, in our context, an exponential speedup of the overall algorithm is not to be taken for granted, as the nature of the data may require a computationally expensive initialization of the quantum state.…”