# Quantum fourier transform

**How would the circuit look like for only 1 qubit?**

For only 1 qubit the QFT algorithm contains only one Hadamard gate.

**In the 2 qubits system, what would be the result of the following expression?**

**QFT _{2}( |0> + |2> )**

Actually,

QFT_{2 }( |0> + |2> ) = ( |0> + |2> )

as a middle step, you can show that

QFT2|0> = 1/2 ( |0> + |1> + |2> + |3> )

and

QFT2|2> = 1/2 ( |0> - |1> + |2> - |3> )