Quantum Information for Quantum Cats (19)

Quantum Circuit ; Three Qubit Operator

Something has to be done to achieve "and" operation. The easiest possibility isto add one more qubit both to input and output channels. We consider the following transformation on three qubits state

This operation is a three qubit extension of Cntl-NOT, and it operates as .not. unit to the lowest qubit if and only if higher two qubits are both 1.

Thus the name Control-Control-Not. Formally, we define it as

If we set z=0, we have

So the awaited AND is here!

Moreover, we have

which means that Cntl-NOT and NOT is achived as a special case of Cntl-NOT. So, with Cntrl-Cntl-NOT, we can produce any circuit we want, and CCN is a universal quantum circuit element

Some of you migh have a question "Nice theory! But what abou the actual realization on devices?" Well, you will make a very good experimental physisist! (Or maybe you are already one.) The experiments are underway at laboratories around the world. For now, just imagine that there are microscopic devils who follow our order and manipulate the qubits, propably in exchnage of our soul.