# New mode of Quantum and - or gate

I’m Aurelio, a computer engeneering student and I would propose a new quantum gate that maybe could be interesting to implement and use. I don’t know if such idea is already known but I have not found nothing similar in the internet and I would talk about it. I started trying to obtain a quantum version of classical AND gate. Soon I understood that is impossible to obtain a quantum AND with only 2 bit because of the irreversibility of this kind of functions. Then I introduced another bit and come to this result:

I would name this gate M gate and it respondes to this logic table:

Z A B Z' A' B'
0 0 0 0 0 0
0 0 1 1 0 1
0 1 0 1 0 0
0 1 1 0 1 1
1 0 0 0 0 1
1 0 1 1 1 0
1 1 0 1 1 1
1 1 1 0 1 0

Z,A and B are the inputs qbits while Z',A',B' are the output qbits:

• when Z qubit in input is in state |0> , the output will be : {Z' = A xor B, A' = A and B, B' = B}

-when Z qubit is equal in |1>, the output of the gate will be : {Z' = A xor B, A' = A or B, B' = not B}

As you can see Z qbit act as a control bit and with only this gate we can express all principal logic operations in one time.(XOR,AND,OR,NOT) Implementing this gate we could resume the behaviour of all this operations.

The corrisponding matrix of the M gate will be: |X |X |X |X |X |X |X |X | |:--|:--|:--|:--|:--|:--|:--|:--| |1|0|0|0|0|0|0|0| |0|0|0|0|0|1|0|0| |0|0|0|0|1|0|0|0| |0|0|0|1|0|0|0|0| |0|1|0|0|0|0|0|0| |0|0|0|0|0|0|1|0| |0|0|0|0|0|0|0|1| |0|0|1|0|0|0|0|0|

Is simple to verify that the matrix is unitary and so it rappresents a valid reversible function.

Can this gate be usefull in order to add a layer of abstraction to quantum computing? Was it already known or I found something new? Can it be used to solve some known problem ? What appens if Z is in a super position?