12.6 Parameterized circuits
The Z gate is fixed in the amount it rotates around the z-axis, while the general Rφz gate has the variable parameter φ. When we include such a gate in a circuit, we get a family of circuits that vary with φ. We need such circuits for NISQ algorithms, and we have seen examples of them before.
In section 10.1.3, we developed the circuit for the Quantum Fourier Transform on three qubits and denoted it QFT3. circuit$parameterized
The z-rotations follow a pattern, with angles equal to π divided by powers of 2.
Let’s add a parameter t to the rotation angle, as shown in Figure 12.18. When t = 0, each rotation gate is trivial and is the ID gate. When t = 1, we have QFT3. We call this circuit with a single parameter U(t).
