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Why the operations need to be reversible

Well, as far as I know, it goes back to the Landauer’s principle. It talks about the erasure operation dissipating some energy. What does that mean? It means that if you do some logical operations on the Qubits, like And/Or whatever that we can do on normal bits, they have to be reversible; meaning that you should be able to get the initial values out from that operation as well. If you lose the value you have created some heat, meaning that you have spent some energy. Why should I care about that? Well, you do quite a lot of operations with Quantum Computers, right? If you need to spend energy for each operation that is a lot of heat and energy, hence lots of money. You don’t wanna spend that for sure!

How to make the normal operations reversible? There is a gate called Toffoli gate which helps us with that. How? Consider the NAND operation: A NAND B is {\displaystyle {\overline {A\land B}}} (https://en.wikipedia.org/wiki/NAND_gate).
The problem with the normal NAND is it does not preserve the A and B values. To be able to solve that problem, we should consider three qubits a,b,c. These three Qubits go into a Toffoli gate and it flips the third gate if the first two are 1. So if we set c to 1, and a and b are 1 as well, then the output of that gate is the NAND of a and b.

So with that we made sure to not, in theory, spend zero energy to do our calculations. To make sure that it happens, you just need to reverse all the computations that you did on the qubits after the result is retrieved.(Not my theory 🙂 Bennet said that)


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