Comparator

 I started the day windering if one might do subbbbbtraction on a quantum

computer, using two's complement. Turns out there already is a built subtraction

of tis kind, in the comparator() function.

So what is two's complement. With binary numbers, one subtracts one number 

form the other by flipping the elements of the lesse number, adding 1 to it. And

adding the two numbers. the result - from which the last carry is discarded - is the

answer.

8 - 5 converts to 1000 minus 0101

Flipping 0101 gives 1010

Adding 1 gives 1011

Adding the two numbers is 1000 plus 1011, and discarding the most significant carry =

1011 + 1000 = 0011

And that is 3, the correct answer...

Below, the comaparator function in action:

                                                        

The code was fully worked out on QuantumComputingUK.org. But it was not

usable without an upgrade to current Qiskit usage. I was somehow convinced that

one didnt transpile code for the simulator, just for an actual Qcomputer. Perplexity

generated the new code elements I needed...