Chapter 12 - Quantum machine learning

Abstract

This chapter covers machine learning (ML) and quantum machine learning (QML). It begins with a review of the classical supervised, unsupervised, and reinforcement ML algorithms and then discusses principal component analysis, support vector machines (SVMs), clustering, boosting, regression analysis, and neural networks. The focus then moves to QML algorithms, first describing the Ising model and relating it to quadratic unconstrained binary optimization (QUBO) problems. We then study how to solve QUBO problems by adiabatic quantum computing and quantum annealing. To perform QML using imperfect and noisy quantum circuits, we describe the variational quantum eigensolver and quantum approximate optimization algorithm (QAOA). The impact of the QAOA is illustrated through combinatorial optimization and MAX-CUT problems and solutions. Next, quantum boosting is discussed and related to QUBO problems. Quantum random access memory is described next, where we address the superposition of memory cells with the help of a quantum register. Quantum matrix inversion, also known as the Harrow–Hassidim–Lloyd algorithm, is then described. Quantum principal component analysis, one of the many QML algorithms for which quantum matrix inversion is a basic ingredient, is also described. In the quantum optimization-based clustering section, we describe how the MAX-CUT problem is related to clustering and can thus be solved by adiabatic computing, quantum annealing, and the QAOA. Grover algorithm-based quantum optimization is discussed next. The quantum K-means section describes how to calculate the dot product and quantum distance, followed by the Grover search-based K-means algorithm. In the quantum SVM section, we formulate the SVM problem using least-squares and solve it via quantum matrix inversion. The section on quantum neural networks (QNNs) describes feedforward QNNs, quantum perceptron, and quantum convolutional networks.