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Neo is not intrinsically any more quantum-proof than any other blockchain that uses Elliptic Curve Cryptography (but note that the odds of quantum computers causing issues are lower than people think they are). On the other hand, Neo has previously proposed NeoQS (Neo Quantum Safe), a Lattice-based cryptographic approach that, if/when implemented, would make the already low practical risk even lower:
State-of-the-art studies and reports indicate these classes of problems, with specific pre-defined conditions, are able generate NP-Hard instances of these problems even in the worst case. However, some other properties were not accomplished, such as revealing parts of the secret after signing. Thus, for accomplishing the requirements of a complete cryptographic system, the mechanism should be able to sign $N$ messages without disclosing information about its secret. Currently, some slightly different variants are being proposed such as Learning with Errors (LWE) and its compact version known as Ring Learning with Errors (R-LWE). (link)