Is there a formalization of the computational model for quantum computers? There are several equivalent computation models, each capable of simulating each other. For example, the lambda calculus or the SKI calculus which are based on rewriting, Cardelli's object calculus, Hoare's communicating sequential processes, and of course the universal Turing machine, all of them formally defined.

I do understand that though there are possibly different ways of building quantum computers, the ways we build them today are Turing-complete and equivalent to the other models of computation. My question is: have anyone formalized a mathematical computation model for a quantum computer (such as the D-Wave)? (As the other models, I assume this could be used as a programming language.)

(I do understand that a possible answer would be "the quantum mechanics", but that's not exactly what I'm looking for...)
Yes.  The quantum Turing machine is a mathematical formalization of a computation model for a quantum computer.

See also https://en.wikipedia.org/wiki/Quantum_computing#Developments and https://en.wikipedia.org/wiki/Quantum_complexity_theory and https://en.wikipedia.org/wiki/BQP.