The most ambitious one imho is qbitcoin[1]. It's based on quantum teleportation and quantum digital signatures. That gives it quite a low Technology Readiness Level[2], but hey, we see articles about actual implementation of quantum teleportation everyday, so who knows?

1. https://arxiv.org/abs/1708.04955

2. https://fr.wikipedia.org/wiki/Technology_readiness_level

Two examples I know of are: https://github.com/metacurrency/holochain/wiki/FAQ and http://bitlattice.org/

Although I'm far from being knowledgable enough to know the disadvantages of these methods in relation to blockchain nor whether they can really deliver on their claims. From what I've learned, my intuition says they're more suited to the task - could be a wrong impression though, hope someone here more knowledgeable on the subject could expand on it.