Chapter 12
Quantum Kernels and Quantum Two-Sample Test
In this chapter, we discuss the possibility of achieving quantum advantage on one of the most fundamental problems of quantitative finance – classification of the probability distributions. The problem can be formulated as follows. Let us assume that we have two sets of samples (either ordered or not), in the most general case of unequal size, drawn from the unknown multivariate probability distributions. Can we say with the desired degree of confidence whether these samples were drawn from the same probability distribution or not? This problem has many direct applications to the practical use cases, especially on the buy side, such as time series analysis, detection of structural breaks, and monitoring of alpha decay, to name just a few. The problem of comparing multivariate probability distributions given by two datasets is known as a two-sample test. We already mentioned one such test in Chapter 9: the Maximum...
