Quantum Computing for Inference

Abstract

After the discussion of classical-quantum interfaces, we are now ready to dive into techniques that can bee used to construct quantum machine learning algorithms. As laid out in the introduction, there are two strategies to solve learning task with quantum computers. First, one can try to translate a classical machine learning method into the language of quantum computing. The challenge here is to combine quantum routines in a clever way so that the overall quantum algorithm reproduces the results of the classical model. The second strategy is more exploratory and creates new models that are tailor-made for the working principles of a quantum device. Here, the numerical analysis of the model performance can be much more important than theoretical promises of asymptotic speedups. In the remaining chapters we will look at methods that are useful for both approaches. This chapter will focus on the first approach and present building blocks for quantum algorithms for inference, which we understand as algorithms that implement an input-output map y = f (x) or a probability distribution p(y|x) of a machine learning model. We will introduce a number of techniques, tricks, subroutines and concepts that are commonly used as building blocks in different branches of the quantum machine learning literature. The techniques rely very much on the encoding method, and the language developed in the previous chapter will play an important role. The next Chap. 7 will look at training, or how to solve optimisation problems that typically occur in machine learning with a quantum computer. Chapter 8 considers the exploratory approach more closely and looks at genuine quantum models such as Ising models, generic quantum circuits or quantum walks, and shows some first attempts of how to turn these into machine learning algorithms. 6.1 Linear Models A linear model, presented before in the contexts of linear regression (Sect. 2.4.1.1) and perceptrons (Sect. 2.4.2.1), is a parametrised model function mapping N-dimensional inputs x = (x 1 , ..., x N) T to K-dimensional outputs y = (y 1 , ..., y K) T .