# What is the point of building arithmetic circuits in a quantum computer?

My question simply is the following: is there any interests in building arithmetic circuits such as adders or multiplier on a quantum computer?

I'm asking this because it seems that classical computers are way better at doing arithmetic operations, so even if a quantum algorithm needs to do some arithmetics, wouldn't it be better to let a classical computer handle this part and then return the results to the quantum computer so it can then continue to run the algorithm?

• if you want to use the result of the calculation within part of a larger computation. You cannot just farm this out to a classical computer due to linearity. Fine, if the QC is guaranteed to be in a basis state $$|a\rangle|b\rangle|0\rangle$$ then you might think you could prepare $$|a\rangle|b\rangle|a\oplus b\rangle$$ by computing $$a\oplus b$$ and just making the state. But if any of the registers are in a superposition, you would be unable to read all the values, and unable to prepare a suitable superposition. The calculation has to be done within the quantum computer to preserve the linearity of the operation. It might be defined on computational basis states, but must work just as well for superpositions.