9.2 From gates to circuits

A quantum register is a collection of qubits we use for computation. By convention, we number the qubits in the register as q₀, q₁, …, q_n. All qubits in a register are initialized to state |0⟩.

A quantum circuit is a sequence of gates applied to one or more qubits in a quantum register.

In some algorithms we group qubits into one or more labeled registers to better delineate their roles. It’s common to have an ‘‘upper register’’ and a ‘‘lower register,’’ for example. [20, Chapter 2]

Let’s look at some simple example circuits to see how they are put together and what the components are called.

9.2.1 Constructing a circuit

The simplest circuit is

Here qubit q₀ is initialized to |0⟩ and we do an immediate measurement. |m₀⟩ holds its measurement state which, of course, must be |0⟩...