I understand what a qubit-based quantum computer by the current definition is and how they are constructed. I read another thread where someone suggested encoding a computation into a dual-slit experiment and reading out the answer as interference vs non-interference, and this was mostly shot down since it's not "useful", because the system ceased to be a quantum computer when decoherence occurred.
But this reminded me of an old idea I had on other ways to encode computations in physics than the "classical" qubit-based schemes. As a striking example, consider one of the canonical uses for a quantum-computer - to efficiently simulate quantum-level systems. Well - to do this without a quantum-computer, you could actually assemble the system itself and let it "run", and then read out what you were looking for to simulate in the first place in many cases, in a vastly more simple way than digitally calculating it with qubits. Is this then not also a "quantum computation", really? The closest analogue I can come up with is the way analog computers were designed before digital computers took over, and that they were indeed much more efficient at a certain class of problems.
Even a system of 3 particles performs a calculation (of sorts) which is difficult to simulate traditionally.
More generally, if you could encode your problem into a hamiltonian which you subsequently map onto a physical structure wouldn't this be very useful? You might not be able to run algorithms on it, but you might be able to format the problems the algorithms were meant to solve in the first place. I'd be interested in hearing if this approach is pursued and I have missed it or if it is deemed to be useless for some reason, or if it's useful but "digital" quantum computation is simply more attractive in the long-run so most of the focus is on that. Maybe there is a measure on the computational complexity that can be mapped or performed by a general quantum structure (non-qubit-based)?
I seem to remember a Canadian company called D-Wave which I think do this more or less, and there was (is) much heated discussions on if it was "real quantum computation" or not.
EDIT: Nature published a special Nature Insight review on this in April 2012, especially about Quantum Simulators, where the issues I brought up in this question are discussed, including the "digital vs analog quantum computation" issue.