Quantum Information for Quantum Cats (21)

Quantum Circuit : Quantum Summation

We now want to construct something useful out of the quantum circuit elements we seen so far. The most basic of algorithm has to include the addition of two numbers. The addition of two one bit numbers generaly becomes a two bits number. If we write the two one bits as a and b, and the added number c = ( c1, c0 ) , we have

We first note that we can duplicate arbitrary state | a > with the use of Cnt-Not as shown in the right.

With this, we can have two sets of ( a, b) that is to be fed into the calculation of c1 and c0 separately.

The higher bit c1 is calculable by .and operation made up from CCN, and the lower bit c0 is calculated with .xor. which is made by Cntl-Not. The resulting circuit diagram looks like this:

The construction here should be easily extendable to addition of arbitrary n bits. Try out by your own with the n=2 bits case!

This construction uses five qubits in total, which seems to include some redundancy. In fact, it is possible to reduce this construction into the one with only three total qubits. This would be another good excersize for readers.