Which Masters is right for me? I am an undergraduate student in Canada doing a double degree concurrently, a B.Sc (Bachelors of Science) and a B.Eng (Bacehlors of Engineering) over 5 years. (8 years down to three at the price of my sanity? Sure haha!).

My Major in Science is Physics, and my Discipline in Engineering is Electrical/Computer. 

When it comes to picking my masters, I have three options:


M.Sc (Science, thesis based)
M.A.Sc (Applied Science, thesis based)*
M.Eng ( Engineering, project based)


From knowing nearly nothing about these, I think the M.A.Sc sounds right for me, sort of a "middle ground".

I want to go on study quantum computers, specifically to apply the principles of quantum field theory to microprocessors and develop quantum computing hardware and software. 
(I work as a computer programmer alongside my studies, and I've been a professional polyglot programmer since I was 16, and a hobbyist since I was 11)

My question is, which masters would help me more on a path to a Ph.D, and eventually to a job in academia? 

A fellow undergrad suggested I do a double-masters to compliment the double-degree, is this possible? Would it be useful to me at all?
When it comes to picking my masters, I have three options:
  
  M.Sc (Science, thesis based)
  M.A.Sc (Applied Science, thesis based)*
  M.Eng ( Engineering, project based)


The letters in your masters degree do not matter. In other words, you'll never see an M.Sc. or an M.Eng. specifically asked for in an application call ... you'll only ever see "Masters". As such, your degree could be called an M.Xk.Cd. and nobody would really care. It's the topic and quality of your masters matters most! 

If you want to work on quantum computing, then you should look for a good masters programme in either Computer Science, Electrical Engineering or a relevant field of Mathematics. These are typically M.Sc. or M.Eng. courses (again, not that the letters matter!). 

A research masters is usually preferable, in that you may even get a publication or two which will help with PhD applications ... or you may continue in the masters programme and graduate into a PhD programme if you are happy with your supervisor.

On a side note, I would encourage you to be flexible in your interests. You quote "quantum computing" as an interest but it can often be unfeasible to get a PhD you like in a really specific area. I think at this stage it's important for you to decide what discipline you want to pursue (Comp. Sci., Maths, Physics, etc.). Having a sub-field in mind is great, but don't plan your future too rigidly around that.


  A fellow undergrad suggested I do a double-masters to compliment the double-degree, is this possible? Would it be useful to me at all?


Of course it would be useful. :) 

But as to whether it would be worth your time, I would say absolutely not. See (1).

(1) Masters + 0.5 × PhD ≫ 2 × Masters