Earlier quoted context omitted.
The difference between QC and all those other examples of interference is that, in the case of QC, the interference happens in configuration space rather than ordinary 3-dimensional space. And configuration space is enormous ; it has a dimension that grows exponentially with the number of particles. The number of paths that could interfere with each other to produce a given amplitude is likewise exponential (in that…
Out of all your replies, I THINK that this is the one that helped me grok why QC is different than somehow simulating quantum math in a classical computer. The idea of being able to tap into more than 3 dimensions sounds like something very fundamental, kind of like relativity, and a key aspect of how our universe works that at least I was never aware of (and probably a lot of other people!) Would you consider writin…
Re: I'm Scott Aaronson, quantum computing/computational complexity researcher. AMA
#371Pretty much any intro to QC (and in particular, any of the intros I've written, and linked to elsewhere on this thread) will make the point about Hilbert space (that's what it's called) having a dimension that grows exponentially with the number of particles in your system. This is because every possible classical configuration of the system is its own orthogonal "direction" in Hilbert space, and the full state can be an arbitrary superposition (i.e., complex linear combination) of those directions.