SHA3-256 is and will remain quantum-proof for an extremely long time according to University of Waterloo | Consensus Décentralisé - Blockchains - Smart Contracts - Decentralized Consensus | Scoop.it

While it's reasonable to assume that a world with real quantum computers will ruin traditional asymmetric encryption, perhaps surprisingly hash functions might survive.

That's the conclusion of a group of boffins led by Matthew Amy of Canada's University of Waterloo, in a paper at the International Association of Cryptologic Research.

The researchers – which included contributions from the Perimeter Institute for Theoretical Physics and the Canadian Institute for Advanced Research – looked at attacks on SHA-2 and SHA-3 using Grover's algorithm (a quantum algorithm to search "black boxes" - Wikipedia).

They reckon both SHA-256 and SHA3-256 need around 2166 “logical qubit cycles” to crack.

Perhaps counter-intuitively, the paper says the problem isn't in the quantum computers, but the classical processors needed to manage them.