IEEE Spectrum has an article by Dr Massimiliano Versace about a memristor-based approach to AI that consists of a chip that mimics how neurons process information.

Researchers have suspected for decades that real artificial intelligence can't be done on traditional hardware, with its rigid adherence to Boolean logic and vast separation between memory and processing. But that knowledge was of little use until about two years ago, when HP built a new class of electronic device called a memristor. Before the memristor, it would have been impossible to create something with the form factor of a brain, the low power requirements, and the instantaneous internal communications. Turns out that those three things are key to making anything that resembles the brain and thus can be trained and coaxed to behave like a brain. In this case, form is function, or more accurately, function is hopeless without form.

Basically, memristors are small enough, cheap enough, and efficient enough to fill the bill. Perhaps most important, they have key characteristics that resemble those of synapses. That's why they will be a crucial enabler of an artificial intelligence worthy of the term.