Can the idea of quantum computing be simplified/abstracted to say instead of doing binary (0 1) calculations, it do does calculation on arbitrary base? E.g. base 16 (hex) or base 1024?
If this is true, it would be easier to code, and compilers could spit out very efficient machine code.
Yes, base has nothing to do with anything, talking about "qubits" is just a convention since computation is usually thought of in terms of bits. The fundamental idea of a quantum computer though has nothing to do with binary in particular. Same as for classical computers.
It's not clear to me why you claim this would be related to efficient machine code, though.
Current "digital" microchips use electric "on" (1) and "off" (0) and base 2 (also called binary) mathematics is used.
Someone explained me quantum mechanics that it supports more states, not just on (1) and off (0), that it can have dozens or hundreds of states. Is this correct / state-of-the-art understanding?
I imagine how cool it would be to have more states, not just 0 and 1. A computer running on more states could encode machine code in fewer instructions, so it could calculate more with the same frequency.
So why downvote me? Either explain me where I got something wrong, or skip it in case you know less than me.
> Someone explained me quantum mechanics that it supports more states, not just on (1) and off (0), that it can have dozens or hundreds of states. Is this correct / state-of-the-art understanding?
No, that's not really correct. Being able to put states in superposition is very different from having more classical states.
> I imagine how cool it would be to have more states, not just 0 and 1. A computer running on more states could encode machine code in fewer instructions, so it could calculate more with the same frequency.
That doesn't really make any sense. A cycle is still a cycle. How many instructions you can encode with a given length doesn't tell you anything about how fast they execute.
Even going with an extremely charitable reading, I don't think there's any way anything that you're talking about could lead to anything better than a constant-factor speedup (and not a large one). The point of quantum computing isn't to get mere constant-factor speedups. Such a thing would be insignificant in comparison to what quantum computers can actually do.
If this is true, it would be easier to code, and compilers could spit out very efficient machine code.