Mark Webber and his team at the University of Sussex in the UK recently calculated that breaking the cryptography in a 10-minute window would require a quantum computer with 1.9 billion qubits, while cracking it in an hour would require a machine with 317 million qubits. All of this would need to be well-timed and finished in a relatively small time window, which sounds hard but it is worth doing because it puts every Bitcoin transaction at risk. They would then need to get their bogus transactions processed before the original transaction (by paying a bigger fee).
An attacker with a quantum computer can find the corresponding private key and recreate the transaction to send the money (for example) to themselves. When you spend Bitcoin, you broadcast your public key. A further and much bigger risk to Bitcoin is the attack on unprocessed transactions. Remember that’s just for the lost or abandoned vulnerable wallets. With Bitcoin hovering around $30,000 or so, that means a pot of more than a hundred billion dollars is at the end of the quantum rainbow. For technical reasons to do with the way that public keys and things work, the accountants Deloitte reckon that about four million Bitcoins will be vulnerable to such a quantum attack. One of these problems is, of course, breaking the asymmetric cryptography at the heart of cryptocurrency in order to transfer money out of lost or abandoned wallets. Such a system will have enough logical qubits that the system will be able to execute powerful algorithms to attack problems that are beyond the capability of classical supercomputers. Professor John Martinis, who used to be the top scientist in the Google GOOG quantum computing team, says that Google's plan in this field is to build a million-qubit system with a sufficiently low error rate that error correction will be effective enough to make execution reliable about a decade from now. The code-cracking quantum computers that will be needed to find them are under development but they won't happen tomorrow. It won't be archeologists looking for these quantum computers, of course, because a great many other people (eg, organised crime, unscrupulous "whales" and the tax authorities of many nations) are searching for them too. When quantum computers break the encryption behind the digital signature schemes used for (for example) Bitcoin BTC and Ether ETHeum, then people will be able to spend each others’ money with impunity. In time, new technology will come along to mean that they can be recovered, except in this case it will be a quantum computer rather than a submarine.
Those gold coins spread over the South American seabed remind me of all of those bitcoins that have gone to crypto-heaven, or perhaps crypto-purgatory, because the relevant private keys have been lost.