Are the current implementations of blockchain resistant to attacks using quantum computation?
Resistant against near-term technology? Sure.
Reliably secure in the long term? Probably not.
Will this pose a major problem? Very likely not.
Is this risk unique to blockchains? Nope.
Because even if quantum computers would become a major threat to current implementations, the community could just elect to do a hard fork to post-quantum cryptography.
Not to say that blockchain technology developers and researchers don't need to worry about working on this issue, though I'd imagine that the average user needn't be concerned with this particular threat.
Also worth noting that other financial institutions, including banks, would be prone to a similar risk in some weird hypothetical world in which people inexplicably elected against upgrading their crypto. For example, hackers could use quantum computers to crack a financial institution's TLS/SSL certificate, allowing them to man-in-the-middle attack (random 2015 paper).
Here's a 2017 paper that projects that Bitcoin could potentially become vulnerable by 2027, using generous assumptions:
The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk are cryptocurrencies, a market currently worth over 150 billion USD. We investigate the risk of Bitcoin, and other cryptocurrencies, to attacks by quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.
–"Quantum attacks on Bitcoin, and how to protect against them" (2017-10-28)
That said, I'm not too sure how relevant a concern this might be in practice as it seems like that the situation'll change before that point. Even if Bitcoin's still around and going strong by the time it could be attacked, various mitigation techniques might go into effect.
The "Weakness" article on Bitcoin's wiki doesn't even mention quantum stuff, though their article on "Myths" does:
Quantum computers would break Bitcoin's security
While ECDSA is indeed not secure under quantum computing, quantum computers don't yet exist and probably won't for a while. The DWAVE system often written about in the press is, even if all their claims are true, not a quantum computer of a kind that could be used for cryptography. Bitcoin's security, when used properly with a new address on each transaction, depends on more than just ECDSA: Cryptographic hashes are much stronger than ECDSA under QC.
Bitcoin's security was designed to be upgraded in a forward compatible way and could be upgraded if this were considered an imminent threat (cf. Aggarwal et al. 2017, "Quantum attacks on Bitcoin, and how to protect against them").
See the implications of quantum computers on public key cryptography.
The risk of quantum computers is also there for financial institutions, like banks, because they heavily rely on cryptography when doing transactions.
Regarding the point about updating mentioned above, it's that while Bitcoin and other blockchains do tend to require standard algorithms that may be foreseeably attacked by quantum computers, before that's an issue, they can basically just do a hard fork, which is basically an update that everyone in the network migrates to, enabling stuff like algorithm changes.
What is 'Hard Fork'
A hard fork (or sometimes hardfork), as it relates to blockchain technology, is a radical change to the protocol that makes previously invalid blocks/transactions valid (or vice-versa). This requires all nodes or users to upgrade to the latest version of the protocol software. Put differently, a hard fork is a permanent divergence from the previous version of the blockchain, and nodes running previous versions will no longer be accepted by the newest version. This essentially creates a fork in the blockchain: one path follows the new, upgraded blockchain, and the other path continues along the old path. Generally, after a short period of time, those on the old chain will realize that their version of the blockchain is outdated or irrelevant and quickly upgrade to the latest version.
–"Hard Fork", Investopedia
Of course, pushing a hard fork requires getting much of the community to accept it, though since pretty much all members of a cryptocurrency network wouldn't want to get hacked/scammed/etc., a hard fork pushed to avert a foreseeable risk of attack by quantum computers would almost certainly be uncontroversial.