Is there any difference in effect between a quantum circuit and a carefully constructed analogue one relying on interference? For example, why couldn't I take a series of $N$ carefully shaped pipes, split a sound source between them, and build, say, a quantum Fourier transform circuit with classical versions of Hadamard and phase shift gates? For example, it would be easy to shift phase by extending the length of a pipe with a sufficiently smooth spiral. I recall that you can invert the phase with a reflection or a phase shift set to 1/2 the wavelength of the sound in the pipe. You could split and combine outputs by splitting and combining pipes. Then, instead of tallying up clicks on different channels (as in a quantum computer), you could just measure the power coming through each of the output channels.
I'm not saying this is necessarily practical--if nothing else you'd obviously have better bandwidth at higher frequencies than sound could propagate through most media. I got the sense there had to be some difference in effect between this hypothetical scenario and a real quantum computer. Could anyone help identify it or else confirm the effect is, in fact, the same?