All of quantum computing is done with strictly reversible logic. But this is not a reduction of power. The Toffoli gate is an example of a reversible 3-bit logic gate that is universal. You can transform any classical circuit into a reversible one using this gate.
The trick? You have some input/output wires in your circuit that start with initial value 0 or 1, and some that end up in a 'garbage' state. You don't care about what they end up with, they strictly exist to maintain reversibility.
As an concrete example, the binary operator a OR b is not reversible - it destroys information. But if we make it a three-in three-out operator f(a, b, c) -> (a, b, c XOR (a OR b)), then it is reversible. Here f is it's own inverse, because applying it twice you'd end up with c XOR (a or b) XOR (a or b) = c.
Yet if you start with c in an initial 0 state, you can now compute the binary OR of two variables a, b in a reversible manner.
The trick? You have some input/output wires in your circuit that start with initial value 0 or 1, and some that end up in a 'garbage' state. You don't care about what they end up with, they strictly exist to maintain reversibility.
As an concrete example, the binary operator a OR b is not reversible - it destroys information. But if we make it a three-in three-out operator f(a, b, c) -> (a, b, c XOR (a OR b)), then it is reversible. Here f is it's own inverse, because applying it twice you'd end up with c XOR (a or b) XOR (a or b) = c.
Yet if you start with c in an initial 0 state, you can now compute the binary OR of two variables a, b in a reversible manner.