Sure, but you might as well use the internet instead.
If you have chips that can convert thoughts into electromagnetic signals, then you've already done the hard part. No need to complicate things by trying to encode that information into quantum states - just encrypt it and send it over Wi-fi. Or if your recipient is very far away, like light-years away, just send it to a radio terminal that beams your thoughts toward them through space.
The main issue with using quantum teleportation instead is that you can't just transmit the quantum data by itself. You actually have to send some signal to the receiver chip to tell it how to build the teleported matter at the other end. So effectively, any quantum processes happening here are redundant.
Forgive me for speculating, but there are only a few reasons I can think of that someone might want to use quantum teleportation in place of electromagnetic waves, and all of them are myths.
- Myth 1: Quantum teleportation is more secure.
This is the most plausible explanation, but even in a society with quantum computers, most quantum researchers would tell you that there are still probably ways to encrypt information sent online without quantum computers being able to unscramble it (i.e. elliptic curve cryptography).
- Myth 2: Quantum mechanics has something to do with consciousness.
I don't know where people get this from, but there's apparently an idea that thought is somehow a quantum phenomenon. Maybe you thought that this would make quantum states a good medium for transferring thoughts? All I can say is, based on our current understanding of neuroscience, this is not true at all. Neurons can be explained perfectly well in terms of classical electrons in a series of charge gates.
Of course, any way of recording and transmitting thoughts is pure sci-fi, so you could just declare that you need a quantum computer to do it. But I'd recommend against it, since it's difficult to write a sci-fi topic well if you don't know the science behind it.
- Myth 3: Quantum teleportation is faster
Again, just speculating, but if the reason you're using teleportation is to send thoughts across space instantaneously, then unfortunately, it won't work. Like I said before, quantum teleportation requires a second, non-quantum signal to complete the information transfer, so it can never transmit information faster than the speed of light.
If you're still dead-set on using quantum teleportation, my only response would be that both thought-transfer and quantum teleportation are technologies far ahead of our current time, so for all we know now, the chips you're describing are possible. However, I hope that my explanation above has convinced you that the element of quantum teleportation doesn't need to be there. As someone somewhat knowledgeable on the subject, its inclusion would have me scratching my head and wondering why conventional electronics weren't used instead.