Building our circuits with the basis gates – U1, U2, U3, and ID

Let's begin by exploring three of the gates that we recognize from Chapter 5, Touring the IBM Quantum® Hardware with Qiskit®. You will not be using these three basis gates, U1, U2, and U3, in your quantum programs. However, they serve as building blocks for all other single-qubit gates when you run your circuits on a quantum computer. In fact, every other single-qubit gate can be written using just the U3 gate. There is nothing explicitly stopping you from using them, but the gate collection that we will go through in the rest of the recipes covers all the ground that we need.

The U gates are not their own inverses

As the U gates perform free rotations around the x, y, and z axes, they are generally not reversible. Adding two of these gates in a row does not negate them unless the rotations add up to complete rotations. For a quick reminder, see the A quick introduction to quantum...