12.1 Cost functions and optimization

Let’s begin with an ad hoc definition of a concept we need when discussing many NISQ algorithms, the cost function, where we defined functions in section 4.1. As you would expect, such a function C computes the cost of something given one or more inputs. We might express the cost in money, work hours, resources consumed, relative health while undergoing a new medical treatment, or any measure of something used or lost. In machine learning, we employ a cost function to measure how close actual data values are to those predicted by a model we construct. optimization function$cost cost$function

In all these examples, we are interested in minimizing the cost function. We want to find when something costs the least money, requires the fewest hours of work or resources, causes the most minor medical trauma or inconvenience, or produces an AI model closest to the training data. This is an optimization problem.

The examples in...