12.5 Time evolution

Another idea we need to understand for NISQ algorithms is time evolution. We begin with some results from single and multivariable calculus, complex analysis, differential equations, and linear algebra. While that is a formidable list of topics, the mathematical objects we manipulate are from Part I of this book. time evolution

Let g be a real-valued function of one real variable t. I chose t because I want you to think of it as the time variable. It is easiest to think of t having values in a continuous portion of R, although it could exclude points where g is not defined. t might take values from a finite set of numbers or a discrete set such as Z. In any case, for two values t₁ and t₂ in the domain of g, with t₁ < t₂, we can consider how g evolves when passing from t₁ to t₂. A common choice is t₁ = 0 and t₂ = 1.

For example, suppose you invest 500 units in some currency in an account that compounds interest continuously at 4% a year. Then...