Asymptotic Improvements in Hardware?

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.

Quantum computers, if they ever get built, will be asymptotically faster than existing computers in certain tasks. Limited quantum computers might already exist, though this is a contentious issue.

StackExchange Computer Science Q#68095, answer score: 6