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QC would break secp256k1, but you don't get the public key to target on chain, you get the hash of it. QC doesn't help there. You could attack TX in the mempool as the spender reveals his public key(s), but you have very limited time to crack them.

If QC are ever built - and that is a big if, not a foregone conclusion - then these networks will react long before the quantum computers are powerful enough to attack.

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I think that changes with Taproot though, otherwise native mutisig would not work. I suppose the mitigation would be to keep high value wallets on hashed public key addresses.

>I think that changes with Taproot though, otherwise native mutisig would not work

Can you elaborate on this? AFAIK taproot only makes it so you don't have to divulge the non-executed branches of code, but everything still uses hashes/ecdsa signatures so the threat model stays the same.

He means with the switch to Schnorr signatures

Taproot exposes a bare public key in each output with spend authority.

Aren’t there already (computationally small) quantum computers right now?

Similar to how a fire cracker is exactly like ICBM, yes.

Even this analogy is generous.

Yes, but none of them have been able to do anything faster than a classical computer can so far. It is not clear it will ever be possible to build a QC that is.

Unless Google has lied about its sycamore processor (or I’m missing something) this isn’t true. I definitely could be missing something though

https://bigthink.com/technology-innovation/google-quantum-co...

It is my understanding that this result is disputed.

Sycamore would probably struggle to factor a two-digit number. Useful quantum computation is still very far away, if at all possible.

The sycamore is really on the border of what current classical methods can simulate. You also need to consider that the funding used for building sycamore was probably orders of magnitudes larger than the funding used to build classical competitors.

Quoting the article, this was on a "highly specific task, one that was specifically designed to give a competitive edge to a quantum computer like Sycamore."

The chose an inherently quantum problem that's difficult for classic computers (including supercomputers) to simulate but matches what the quantum hardware does natively; now we're approaching the stage where quantum hardware can do something more than simulations of quantum hardware. However, that's far from effective 'general purpose' quantum processors that would be capable of executing the quantum algorithms that have interesting implications on cryptography and other fields.

For example, factoring primes - we can brute force e.g. 256bit prime numbers on classical hardware and can't really brute force 1024 bit numbers. That can be done with a quantum computer with 2*n fully entangled, long-term coherent qubits, so a 512-qubit computer (unlike 53-qubit Sycamore) for doing what we can do already and 2048 qubit computer for actually breaking something (or, more realistically 4096 qubit computer for 2048-bit RSA).

secp256k1 is vulnerable under a QC model, though. Discrete log is solvable with Shor's algorithm. Current known quantum computers haven't gotten further than 21 yet, AFAIK.

Without quantum error correction it isn't practical to use them for real world problems.

Scott Aarson wrote a piece that touches on this https://www.quantamagazine.org/why-is-quantum-computing-so-h...

But needing the development of quantum error correction actually invalidates one of the points the article makes:

> Nic Carter pointed out that quantum breaks would be gradual rather than sudden.

It's likely cracking quantum error correction won't be a gradual process. Instead one day it won't work, and the next day it will be possible to build very big quantum computers.

I don't think that means QC will be a major problem for crypto. It's not like there aren't fixes already, and they've proved themselves to be collectively very adept at changing protocols and algorithms. Hell one of the changes they made to bitcoin is to add flag bits and a voting protocol that made future changes easier.

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