# What do empty white circles mean in a quantum circuit?

I'm studying Shor's algorithm. but I see from the beginning this empty circle. what this circle means??

## 1 Answer

It is a "negative" control.

In other terms, the gate in your circuit will apply a NOT on the last qubit if and only if the following conditions are both met:

• $$\vert x_3\rangle = \vert 0 \rangle$$
• the first ancilla qubit is in the state $$\vert 1 \rangle$$.

A "normal" control (i.e. not an empty circle) would change the first condition to $$\vert x_3 \rangle = \vert 1 \rangle$$.

• Thank you very much!! you are so kind :) Have a nice day!! – 유도경 Feb 9 at 7:33