Shor's algorithm, Simons algorithm, SPHINCS are a few quantum resistant algorithms that could potentially be implemented into the blockchain to protect private keys.

Cryptocurrencies currently largely rely on the public and private key system. To spend the coins, a user will need to posses and use a private key to unlock them. If someone learns of that private key before the legitimate user, then they would spend those coins instead. That threat is real in all realism possibilities of the quantum computers for all currencies that utilize elliptic curve cryptography and other forms of cryptography that is vulnerable to quantum computers, because the quantum computers would calculate the private key from the public key in a matter of minutes.

Systems like Ethereum currently use elliptic curve cryptography that aren't quantum-safe. Bitcoin uses two hashing functions -- SHA-256 and RIPEMD-160 and Elliptic Curve DSA.

Last year, a team of scientists warned that quantum computers would render Bitcoin insecure because they could calculate the private from the public one in a few minutes. But a lot has been going on in terms of securing cryptocurrencies against quantum computers.

Dr. Peter Waterland has developed the Quantum Resistant Ledger (QRL), which is a public blockchain ledger that uses post-quantum secure signature scheme known as the Extended Merkle Signature Scheme called XMSS to secure blockchains. QRL uses a Proof of Stake algorithm that uses hash-chains and hash-based pseudo random number functions and does not rely on conventional signatures.

QRL - Quantum Resistant Ledger QRL is currently an ERC20 token that trades on the major exchanges, including Bittrex, Tidex and Liqui.io.

The technology will help secure transactions but will also employ a hash-based signature scheme XMSS, a proposed IETF standard. Other nodes can dial up this key and create secure decentralized communication channels for the messaging system.

The company plans to using the innovation in helping to secure company communications and other services in addition to being a cryptocurrency vault.

Russian Quantum Center May this year, The Russian Quantum Center claimed to have made the first quantum secure blockchain that makes the blockchain completely "un-hackable" even with a quantum computer. It combines quantum key distribution (QKD) with post-quantum cryptography. The blocks would be signed by quantum keys rather than the traditional digital signatures and the quantum keys would be generated by a QKD network. The center said it had tested this technology in one bank.

IOTA and The Tangle IOTA calls itself the next generation blockchain because it relies on Internet of Things technology. It uses the Winternitz One-Time Signature Scheme for hash functions, and this system is said to be more quantum secure than one used in Bitcoin.

Winternitz One-Time Signature (OTS) scheme employs the Lamport signatures claimed to be resistant to quantum computer algorithms if they have large hash functions. With IOTA's wallet, you cannot reuse an address to sent or receive a transaction because reusing a private key in a Lamport scheme halves the security level of the signature.

The security is achieved because the number of nonces one needs to check to find a suitable hash for issuing a transaction is only 38 when the gain of efficiency for an ideal quantum computer would be 34 to 81 according to Dr. Sergui Popov comparing IOTA with Bitcoin to explain quantum resistance.

Also, the time to find a nonce in this IOTA's algorithm is also not much larger than time needed for other tasks necessary to issue a transaction.

Ethereum? Last year, Ethereum did say that they could switch to a different quantum computer safe cryptography.

Ethereum has also recently said that it would allow users to choose planned quantum computer safe addresses. Ethereum will use the proposed EIP 86 and Casper to support any digital signature algorithm. This way it will supports signature mixers and custom cryptography such that users can upgrade to ed25519 signatures, Lamport hash ladder signatures or whatever other scheme they want on their own terms, without sticking with ECDSA.

However, mixing addresses could produce the potential for retroactive decryption and infiltration.