It's not so clear how to securely communicate once an attacker has constructed a large quantum computer and then RSA and ECC are vulnerable due to Shor's algorithm. Probably, this is not likely to happen in the next few years, but I guess Corda is here to stay for a long time too.
Although post-quantum secure Lattice-based signatures have been proposed in the literature, their quantitative security levels are highly unclear. But very recently, practical Merkle-Tree based signatures have been proposed as the 1st practical solution against the upcoming "evil" quantum computer.
If we choose to support at least one post-quantum algorithm, we can focus on Merkle Signature Schemes and be the first Distributed Ledger tech to provide such a security feature.
For those interested on how the basic algorithm works, take a look here: https://en.wikipedia.org/wiki/Merkle_signature_scheme
For more information on a very efficient and practical algorithm, called SPHINCS-256, supporting 128 bits of security and relatively short keys see here: https://sphincs.cr.yp.to/papers.html