9.2 From gates to circuits

A quantum register is a collection of qubits we use for computation. We number the qubits in the register with labels such as q₀, q₁, …, q_–n or q₁, q₂, …, q_n. The quantum system initializes all qubits in a register to state |0⟩. quantum$register circuit$quantum quantum$circuit

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. upper register lower register register$upper register$lower

Let’s look at some simple example circuits to see how we put them together and what we call their components.

9.2.1 Constructing a circuit

The simplest circuit is

We give qubit q₀ the initial state |0⟩, but then...