We'd need artificial neurons without those limitations.

For example, just a few days ago a team from UCSD announced something like that called 'memprocessors'.

Unless it's an actual product, those announcements are a dime a dozen. We're still waiting for "memsistors" and "cold fusion".

It's research, but they claim to have built some.

http://advances.sciencemag.org/content/1/6/e1500031.full

Their conclusion:

"The actual machine we built clearly suffers from technological limitations, that impair its scalability due to unavoidable noise. These limitations derive from the fact that we encode the information directly into frequencies, and so ultimately into energy. This issue could, however, be overcome either using error correcting codes or with other UMMs that use other ways to encode such information and are digital at least in their input and output."

So, it remains to be seen how feasible this machine is.