One of the main benefits of algorithm analysis, is that it offers asymptotic improvements to complexity as opposed to hardware, which offers only constant improvements. E.g switching to a super computer from a workstation might give a $\times 1,000,000$ increase in speed, but if that supercomputer is running a linear search on a sorted array, it will eventually be trumped by a desktop running a binary search for large enough problem sizes.
My question is this:
Are there any improvements in hardware(theoretical or practical) that could offer an asymptotic speedup over pre-existing hardware?
In this case pre-existing refers to at least 3rd generation computing technology. I'm not really interested in speedups over vacuum tubes.