Of course the process of backing a brain up is a bit challenging and not exactly a solved problem. E.g. scanning microscopically thin slices of brain is possible but still magnitudes off in terms of resolution. Also, doing that typically destroys the brain under study.
IMHO it is much easier to backup non organic brains; like proposed in this article. And building those is a lot easier/feasible than it is to pick apart existing ones. With stuff like this and general improvements in electronics, we're approaching the moment where computer systems matching e.g. the neuron count in humans with the equivalent in transistors, electronic neurons are becoming a reality. Backing those up is going to be lot easier.
Which brings me to the point that there's actually only going to be a brief period where electronic brains are not vastly more capable than our own ones. Raises all sorts of interesting questions when you start thinking about that.
The intro section of one of their recent articles is a little meatier than the research site: https://ieeexplore.ieee.org/document/7967719
https://en.wikipedia.org/wiki/Memistor
These are not to be confused with "memristors"; the latter being a two-terminal device, while the memistor is a three-terminal device.
If you look at the original papers describing the ADALINE/MADALINE machines, there's a good description on how these devices were originally made - there's nothing about them that couldn't be duplicated today in one's garage or workshop.
So - if you have a hankering to build your own hardware neural "logic" element...