What's the truth about this "absolutely unbreakable" cipher?
I will go out on a limb here and say that it reeks of snake oil. I have seen the answer by @dirdi, but I am very skeptical. It is clear from the paper that the authors have almost no understanding of cryptography: they refer to algorithms used as DES, AES and RSA, and that quantum computers break them all. 

We know that quantum computers only have quadratic speedup to break symmetric ciphers, to the best of everyone's knowledge. Also the reference to DES, AES and RSA together is very suspect. I quote: "Conventional cryptographic schemes based on DES, AES and RSA encode messages with public and private keys of short length." Huh???

There is no theoretical model for this, like one has for quantum computation (with all of the problems that exist there). Rather, it is more experimental in nature - and we know where that tends to end. Bottom line, this looks really bad and like a lot of other cases where people from other fields think that they can solve all of the world's hard cryptographic problems without knowing anything about cryptography.