Heavy-Abbreviations

We normally model computers as turning machines or lambda calculus. Is there such a model for quantum computers?

Or to ask another way, what does the most basic, complete quantum API look like? What are the functions/classes, inputs and outputs?

Thanks for answering Frank!

Maybe I can put it another way, but don’t the inputs and outputs need to be classical to be useful? Like Shor’s algorithm solves a problem that has no quantum in its description (integer factorization.)

I assume you need a function to construct a qubit, what would the inputs be to that function? And likewise, you need some way to read out the result at the end, so presumably there’s a function that takes a qubit and spits out something classical, like a number or true/false. With those two functions you could create and read quints, but nothing else. So you need a function to manipulate a qubit in a controlled way. What would those functions look like?

Yes, thank you for answering!