@Brain: Actually, Classical physics breaks down all the time to quantum mechanics. Like, hardcore.
		
		
	 
Well, yes, I know that. I'm just saying that the brain is probably completely classical and that the actual usefulness of quantum physics is overstated, regardless of how it functions.
	
	
		
		
			In terms of computing, though, you're mostly correct; quantum computation performs certain types of operations faster than classical, of note being searching and factorising algorithms. The speed issue, however, is actually a significant difference if you're dealing with a changing source material. For instance, if you had a sample that changed itself every X seconds, your analysis algorithm would have to run and output at a faster rate to be useful. So in that sense, increased speed means an actual difference in outcome/applicability. QC's also posited to be able to simulate quantum situations (e.g. solve for the the exact wavefunction of a complex molecule) in ways that a conventional computer can't.
		
		
	 
Additional speed can be useful, yes. But we don't know how useful it might be and we don't know about the overhead.
	
	
		
		
			A conventional computer works on an entirely binary basis; you have two states (usually stored as voltage levels in semiconducting diodes), ON and OFF. In quantum computing, you store information in the energy states of any of a number of structures (my lab, for instance, uses gallium arsenide quantum dots). These energy levels are not merely paired. All quantum computation alogrithms and demonstrations so far have focused on using only two levels to operate on. This australian theoretical paper proposed using a third, higher state, as a way of securing a particular bit of information from gate errors while using CNOT gates.
This opened up the idea of having quantum systems that don't perform binary operations along qubits, but can operate in trinary or higher logic systems, which potentially allows it to perform functions that are not just unfeasible in classical, but impossible. Watch this space!
		
		
	 
I am confused what you mean here. Do you mean binary versus trinary 
operations, which means functions that take two versus three bits? As far as I can tell, CNOT + single qubit operations are universal, so I'm not sure what ternary operations are going to bring to the table, besides marginal efficiency gains.
Do you mean as in three states in a unit rather than two? If so, ternary systems offer next to nothing over binary systems, functionality wise. Take two bits or qubits, juxtapose them, you get a quaternary system, that's all there is to it. A completely analog system would offer next to nothing over a binary system either, because returns decrease exponentially with precision - just allocate enough bits per value and you'll never see a difference. That doesn't mean you can't or shouldn't have ternary systems, but it certainly isn't going to be revolutionary.
The advantage of quantum computation lies in the fact that n qubits do not encode one n-bit value, but indeed a sort of distribution over all 2^n possible values, therefore exponentially more information. Unfortunately, we can only 
sample from that distribution, which typically means exponential time to retrieve all of it, and that's only if we can reproduce it consistently. However, using appropriate unitary transforms in an appropriate circuit, we can entangle and tweak the distributions of the inputs so that sampling from the end result gives the right answer with good probability. Essentially, classical is binary (2^n possibilities), and quantum is "super-binary" (2^(2^n) possibilities), which is a vast improvement despite the gotchas. Binary versus ternary, in comparison, will give you paltry returns.