SPHINCS is essentially Lamport Signatures and SPHINCS+ is essentially removing the need to store “state” by using chains of hashes and a random oracle
https://crypto.stackexchange.com/questions/54304/difference-...
I prefer tham to lattice-based methods because it seems to me that cryptographic hashes (and other trapdoor functions) are more likely to be quantum-resistant than lattices (for which an algorithm like Shor’s algorithm merely hasn’t been found yet).
> Note: Update on April 18: Step 9 of the algorithm contains a bug, which I don’t know how to fix. See Section 3.5.9 (Page 37) for details. I sincerely thank Hongxun Wu and (independently) Thomas Vidick for finding the bug today. Now the claim of showing a polynomial time quantum algorithm for solving LWE with polynomial modulus-noise ratios does not hold. I leave the rest of the paper as it is (added a clarification of an operation in Step 8) as a hope that ideas like Complex Gaussian and windowed QFT may find other applications in quantum computation, or tackle LWE in other ways.