I dont normally come in here but in case anyone is curious I work at a semiconductor plant in Oregon.
I was also a Navy Electronics Technician for 9 years and before that I was in my high-schools electronics club. Actually, I was the president all 3 years.
And before anybody even takes a guess, YES, I played Dungeons and Dragons.
Getting back to the point at hand, with what we currently know about transistors we can only have two states for a bit of data. On and off. Or high and low. Commonly refered to as a 1 and 0 for data purposes.
You cant hold a bit of data with only one transistor. You need two of them, at least. The voltages we have from TTL and CMOS are not written in stone. It used to be between 0 and 5 volts and depending on which type you were using, a given voltage might get you a 1, a 0, or an undefined, which was no good and usually resulted in errors. But you can not get three genuinely seperate states in data. It all has to be ones or zeros because of how the transistors are tied together and hold voltage, which in turn translates to data later on.
In advanced devices like CPU's, they run on much less than a volt. But you still only get 2 usable states.
Also, as an aside, changing from a 1 to a 0 and 0 to 1 causes the transistors to use power, which is why the more times per second you change those states, the more heat you build up.
I.E. the more powerful your device is (CPU, RAM, whatever) the hotter it gets. Thats why we try to use lower voltages and less current in each new generation, to keep the heat reasonable so the devices can be cheaper and used easier.
Also less power draw for portable devices.
I have very little idea on how quantum computers work, but after listening to most of the discussion here on anandtech I can honestly say we shouldnt be too excited just yet. That type of computer theory needs a lot more practice before its useful to the industry.
EDIT: Sorry.
I was thinking DC versus digital in my previous comment. You could get any number of distiguished voltages if you had enough transistors, but (as was already pointed out) all the extra transistors/gates needed to handle that more complicated bit would slow down everything else. You would lose all that performance. Modern processors have billions of transistors already. We have hit many limits as is because we cant make them smaller and fit more of them on a die. At my fab we are using UV lasers and its still not enough to just keep getting faster and faster.
Also as was pointed out, the major change to the math involved in changing 0,1 to 0,1,2,3 would offset the supposed performance increase.
Its kind of pointless. Better to keep it as ones and zeros and just figure ways to make the whole process more efficient.